In prime 2 Samus is hired by the federation to find some missing troops, in prime 3 Samus works with the federation the whole game, not only in the escort mission, so the fact that in other m Samus says that working with Adam in the bottle ship is the first time she works with the federation since she left means the prime trilogy never happened in the canon universe. I obviously acknowledge the prime trilogy as canon but unfortunately nintendo choose other m.

Here's the direct quote from the game, for clarity's sake:

"It was the first joint mission I had been a part of since becoming a freelance bounty hunter"

What Samus does in Prime 2/3 isn't a joint mission. It's being contracted by an organization to do something. If being hired by the Federation to do something that they want you to do qualifies as a joint mission, then basically the entire rest of the series would be non-canon since the Federation hires Samus to root out the Space Pirates on Zebes (the instruction manual states that the Federation hires her) and she's hired once again by the GF in Metroid 2 to exterminate the Metroids. Obviously both of those games are considered canon for Other M's story considering how long it spends banging on about the baby Metroid.

A joint mission is directly working with someone, like how Samus explicitly takes orders from Adam and interacts with the GF troopers for the entirety of her stay aboard the Bottle Ship.

Like I said, in prime 3 she works with the federation the whole game, you can interact and talk to them. Fleet Admiral Castor Dane is the one that gives the orders to samus and the other hunters. In the escort mission Dane gives Samus the order to protect those troops, not to mention during the whole mission other federation troops are fighting against the space pirates. And what about the final assault to phaaze? Sure Samus went to the planet alone but the federation ships opened her the path. So yeah that Samus quote completely disregards the events of prime 3 and in consequence the events of prime 2 and prime 1. You know what the funny part is? without that quote we wouldn't be having this conversation, but nintendo went over themselves thinking Other m was going to take the franchise to another direction. 

That's a good start but it might not be enough to pull me into starting over. (Somehow I biffed and missed the ice beam and I'd rather start over than go and try to find it because I'm dumb like that.)

Honestly, I'd argue that was the last thing Nintendo wanted. I think the quote was put in there with no intention to retcon Prime 2 or 3; honestly it didn't even strike me as troublesome until someone on the internet made a big post about it.

In the end, the only thing I can really say is what I said before; there's a difference between a full blown joint mission and being contracted to do something. Prime 3 is a perfect example of this, honestly. Samus isn't given a superior officer and a checklist of orders she needs to follow at the beginning of the game; instead, she comes into a room with several other bounty hunters, and they are contracted to go find out what's been going on with the Aurora Units. The difference is the level of independence, if you're given an end goal, but allowed to go about achieving that end goal how you see fit, that's being contracted. Jointly working with someone means consistently following their orders and doing things exactly how they say.

I'll grant that the bit on the Pirate Homeworld with guarding the troopers falls more in line with the joint mission aspect (Samus and the Federation working directly with each other), but it's over so quickly I'd say it barely counts as a real mission. Babysitting some Federation troopers for 5 minutes only qualifies as a full joint mission if meeting with someone for 5 minutes to discuss possible romantic interests qualifies as a date night.

As for Phaaze, same deal. Samus isn't working directly with the Federation. The Federation clears a path, and then she does her own thing. If the Federation had, say, gotten her to take part in the actual spaceship fight, receiving direct orders from some captain or something, then that would qualify. But it's not a joint mission unless she's directly working with the Federation itself.

To throw another obscure metaphor out there, think of it this way. Imagine that there's a country suffering from disease that needs medical assistance, but any attempt at sending doctors in is stopped by local insurgents. So, in order to get first aid into that country, a foreign nation gets its military to clear out the insurgency, and then contracts something like MSF to go in and provide assistance. MSF isn't working directly with the army or the nation it's contracted by; there's no direct cooperation between the army and the doctors. That's the sort of situation here; unless Samus is directly aiding the Federation in their current task (i.e. shooting down Space Pirates), then it's not a joint mission.

Tell me, why was Samus surprised that the GF had cloned metroids, space pirates and ridley in Fusion?

Other M destroys the entire Metroid narrative, not just Prime.

To be fair, from what I remember from Fusion, Samus never really expresses surprise at anything except for the fact that there are multiple SA-X.

With that said, yes, Other M throws a wrench into the entire Metroid storyline. I certainly won't debate that. The thing I was discussing is that there's a sizeable number of people who, for some reason or another, have come under the impression that Other M somehow makes the Prime games officially non-canon. There's a particular line that I wanted to clarify the meaning behind.

I don't get the Other M hate. I love the game because, with the exception of intrusive cutscenes, is like playing Super Metroid in 3D. I hope Nintendo release a sequel soon with less cutscenes. And I liked the story.

...assuming this comment is serious, which I'm not entirely sure it is...

The hate comes about because...

-It goes completely against everything we've known about our protagonist's personality to this point.

-The plot is hackneyed, cliched, and tramples all over everything that's part of the Metroid experience. Instead of discovering what's been going on, the game forcefeeds you long cutscenes and monologues where Samus explains everything that's going on. All sense of mystery and discovery is lost. Even if you liked the story, or even if the story was the most riveting tale told, it wouldn't work in a Metroid game. A long, convoluted story that requires a heavy amount of exposition to relay isn't suited for Metroid.

-The character of Samus as well is completely nonsensical based on what we know from previous games. Instead of being a battle hardened bounty hunter who's fiercly independent, she now basically begs for acceptance and to be let in on a Federation mission, even to the point where she's willing to run through an extremely dangerous environment without protective gear just because no one explicity told her she could. She consistently gets outsmarted by dumb conspiracies, makes very amateur mistakes, and in general acts like she's barely been in bounty hunting at all. If you removed the plot elements involving Super Metroid from the game, I'd have probably assumed it took place before Zero Mission or something.

-The side characters aren't much better either. Adam makes extremely poor tactical decisions, like splitting up his entire team throughout the station even when he knows there are bioweapons aboard, continuing to have his team split up after he knows there's an assassin present, not giving Samus permission to use powerups that could not possibly be harmful but could very well be life saving, shooting Samus in the back instead of stopping her like a normal person, and then blowing himself up in Sector Zero instead of trying some alternative method first, like evacuating the space station while setting the self destruct sequence, or getting Samus to fly in and open fire on it. The Deleter's actions make very little sense as well. Trying to take out a legendary bounty hunter with an oversized tractor?

-It's nothing like Super Metroid in 3D. The only similarity I could possibly see comes from how Samus moves, but it lacks the exploration, atmosphere, isolation, and level design of Super Metroid. If I had to list two defining features of Super Metroid, it would probably be exploration and isolation, both of which are essentially non-existant due to the game's extreme linearity and constant messaging from Adam. Past doors are consistently sealed and locked off, even ones from just a few rooms ago, preventing you from exploring anything until the very late game.

-It consistently breaks the bond between the player and Samus. In past Metroid games (with the exception of one brief moment in Fusion that I'm really not a fan of), the only bits of information that were revealed to the player were the ones that were revealed to Samus as well. Other M consistently reveals things to the player that Samus isn't aware of, such as the Deleter attacking MB, Ridley being killed by what turned out to be the Queen Metroid, or that one Asian trooper being offed. You're consistently aware of far more information than Samus is, which negatively impacts both my immersion in the character and the sense of mystery in the game. "Why isn't Adam talking to me anymore?" would be a very interesting question indeed...if the game hadn't revealed to me in a cutscene that he had his earpiece shot off by the Deleter.

-The game itself is unnecessary and just makes the rest of the Metroid storyline very awkward and much harder to believe, particularly Fusion. Instead of Fusion being a believable episode where the Federation tried housing some creatures/Metroids on a space station for the first time and then an X parasite broke out on boards, we now have to accept that the, after the events of Other M, the Federation still thought it was wise to clone Space Pirates, Ridley, and Metroids, and keep them on board some isolated space station, despite the fact that the last time they did so they murdered everyone on board. It makes the Federation look like Weyland Yutani, a cartoonishly evil greedy corporation that just wants to keep its precious aliens no matter how many people they kill, and it makes them retroactively look like an absolute cretin for calling Samus of all people, who knows their secrets, in to investigate when things go wrong.

-The first person "Find it" sections are stupid, obnoxious, halt gameplay for no real reason other than to pad the game's length, and again, break up immersion.

-Switching over to first person for missiles isn't awful, but again, kills immersion and is far more cumbersome than it should have been. In fact, everything to do with using a wiimote exclusively instead of a nunchuk + wiimote combo was a horrible idea.

-The game, despite massively overhauling the mechanics, has very little in the way of original story ideas or new powerups. All of the powerups are simply copypasted in from past games with the exception of the Diffusion Beam (which might as well be since all it did was take the power away from missiles and put it on the beam), the story is ripped straight from Fusion and an awful Aliens fanfiction, and the enemies/bosses are like 80% straight copies from Super Metroid or Fusion. Many times they show up with absolutely no explanation other than "Lol hey guys remember that cool boss? Well we're sticking him in here that makes us cool too right?" Why the heck is Phantoon now an evil space monster that attacks space station's windows?

And there's probably more I've mised. That's why Other M gets hate.

She is in a mission with the federation the WHOLE game, she receives orders in pretty much EVERYTHING she does, she is told what to do and where to go DURING THE WHOLE GAME, the only reason why you think is different is because Adam is such a douchebag he gives the most dumb, irrational orders ever. Samus is independent in prime 3 because unlike Adam, Fleet Admiral Dane respects Samus and he knows what she's capable of, he could behave like Adam and give Samus dumb orders and make her follow them no matter how silly they are because Samus is under federation orders, but he knows Samus has earned respect way beyond anyone in the galaxy, something Adam decides to ignore. Again the only reason you think is different is because Adam is a jerk who doesn't respects Samus. I encourage you to play prime 3 and other m one more time so you can finally see in both games samus is in a Joint mission, the only difference is the way Adam and Dane treat Samus, that completely changes the ways she acts during both games, therefore making you think one is a joint mission and the other one no.