The funny thing is that whether or not he had a proof, it was only definitively proved because he claimed he had a proof, so in a roundabout sense, he's still responsible for the theorem being proved. It's kind of crazy to think about your words carrying so much weight that somebody from hundreds of years in the future will dedicate (a significant portion of) their life to them.
I think he had a hunch, and maybe in his mathematic mind he got to the right answer by the wrong path
But yes had him not pointed it out maybe it would have been relegated to a mathematical curiosity or something
I think there's a deeper (but simpler) reason for it, besides the way Wiles proved it
> he's still responsible for the theorem being proved.
I think you have an odd definition of "responsible". Many (most?) theorems start out as conjectures, and I would strongly disagree that just because someone first formulated a problem that they're "responsible" for the eventual solution.