So, was it a lie or were they just mistaken?

It was a mistake that was blown out of proportion because a ton of people (not just here), just chose to believe it without questioning if it actually made sense.

If that's the case then, how did this mistake come about? I honestly haven't been following this at all. Did Eurogamer get some wrong info from inside sources, Nintendo, or were they just guessing?

So, they themselves say it's 1080p and then they have to "put the rumours from some sources to rest" of it being 1080p... Lol!

The Eurogamer article was written about a month before the whole rumour started, at the same day it released a lot of other websites also ran articles on MK8 so I guess there was a preview event for the press shortly before that. Now Eurogamer either misheard, meant that the game is displayed in upscaled 1080p or just made a typo, whatever it is, after about a month a site picked up this piece of information, didn't bother to fact check even a little (after all at the same day of the Eurogamer article other articles said that the game is 720p) and just ran with it, from there other websites posted the story as well (all btw treating this as fact) and alot of people just believed it.

It does make you wonder why Nintendo didn't just release a Wii HD two years earlier, wich they could probably have sold for $300 and make a profit. Releasing a console of caliber so late really doesn't make any sense.

They lied!

Not the Necropost we deserved, but the one that we needed right now.

I can believe this, it was said to be 1080p & 60fps anyway.

No, they didn't. They are actually right, the game runs at 1080p but upscaled.