Are we sure he was that important for Sticker Star's development? Sure, he made the declaration, but that still doesn't convince me that Intelligent Systems is the main responsible of the Paper Mario fiasco.

Right, but there's a difference between baseless assumptions that don't make sense, and ones that are based on logical observations.
Based on what we know of Miyamoto's history in Nintendo, and human behaviour, do you believe that if Nintendo came to him with an idea and he told them he thought it was a bad idea, that they would still make him work on the project? I very much doubt it.

But honestly, there's no need to debate this point. Because the second point (below) is more interesting, as we have a quote from Miyamoto about it.

I personally am interested in how things came to be, rather than just how they are. If I didn't start analyzing this situation, I wouldn't have learned about the interview where Miyamoto said it was his idea to create a Starfox game based on the Gamepad functions.

I'm not saying he made the game alone, or that he deserves all the blame for whatever people may not like about it. What I'm saying is that he was the one who decided that Starfox should be made as one of the games that would showcase the Gamepad's functions in a profound way.

This imposes some creative restrictions on everyone involved in the development right from the start. They had to make distinct use of the Gamepad's functionality beyond anything we've seen before. Could the rest of the developers have made a better game in spite of that? Maybe. But we have to be sympathetic to the fact that they were working on the game under those conditions.
And the reason this is brought up is because people think Miyamoto is out of touch with what most gamers want these days.
This wouldn't be an issue if Miyamoto was just some random producer/director. But precisely because of his opinion is so valued with Nintendo, it becomes a point of concern for some people.

Last Nintendo gen was best selling console generation ever, so it not exactly fair to compare this gen with it. This gen they had their first HD console with they had lotsa problems and handheld that was very affected by mobile devices.

This gen proved them they cant suport any longer two completly difrent platforms, but its not about they lost touch, its about market that changed, games are today more complex and require more time and resources than ever before, they need far more time for Wii U games than they needed for Wii games not to mention fact that Wii is basically GC with motion controls. Sony also can't support two different platform and that's why they completely abandoned Vita and they totally focused to PS4, are you saying Sony also lost touch!?

Regardless that, here is point about games, and Nintendo definitely did not lost their touch, they made so many great games this gen.

Though I asked you if you think they'd force him to work on a project he considers to be a bad idea.

The one I'm going to cite in my next paragraph.

"SM: We spent more than one year on numerous experiments using the Wii U GamePad, and in the initial experiments, we conducted tests with 3D graphics on screen using Pikmin and Star Fox systems as a trial.

While manipulating the RC aeroplane-like flying experience or creating the mechanism to appreciate the overall and partial views together, it made me think I should continue to create Star Fox utilising these elements. We fixed the basic form in six months, and then commenced the one and a half year development process."

Nintendo had tasked Miyamoto's development team to create games based on the Gamepad. And the idea to have one of the Gamepad focused projects be Starfox came to Miyamoto there.

I'm all for having a productive discussion, but these "How valued?" "How certain?" "Have you worked with Shigeru?" are not going to add any meaningful context to the discussion.
Instead of posing a lot of leading questions, you can just say what you want to say. But these should not be the focal point of your argument.

He rejected their TTYD sequel and forced them to make it into something else that is without story characters etc., how is that not the most important factor?

From what I read, they did a survey at Club Nintendo24 and apparently not everyone was interested in the story, at least when they surveyed Super Paper Mario. And even the devs like Kudo agreed so it appears to be more of a collective thing. This is apparently coming from Iwata Asks so take that for what you will.

That's why we're putting Miyamoto's carreer in context. The higher ups don't have his track record with games. He's considered a genius by his peers, etc.

But if you find it plausible that they would force him to do it even after hearing that it's a bad idea from Miyamoto himself, that tells me what I need to know.

No, just Miyamoto. He said "it made me think I should continue to create Starfox utilizing these elements". I'm talking about who came up with the idea of having Starfox become an actual game as part of the Gamepad project. Not who worked on it.
Because Miyamoto wanted to make a Starfox game that heavily focused on the Gamepad, the developers were forced to design the game around this, whether they liked it or not.

My estimate on how valued it may be is irrelevant.
And you repeatedly asking a bunch of people on Vgchartz if they've worked with Miyamoto is pointless as you already know what the answer will be.