Yeah they kinda do. The canon of a game is the sole property of the company that owns the francise. If Bethesda were to lose Fallout, a new company would decide canon, and they could make anything they wanted not canon and we would have to go along with it (be it Fallout 3 or whatever).
If Bethesda were to do that then it would be the end of the Fallout francise, so they would never do that.
But if they were to do it, their additions would be canon. Like it or not.
2 out of the 3 groups you listed that "determine canon" are basically Bethesda. The other one ("Fans") don't really decide canon at all, we can speculate on and interpret parts of established canon or things that were left a bit unclear, but we do not decide canon. Otherwise the fan fiction section would be filled with "canon" stories.
Can you tell me one instance where what a fan said or did facilitated a formation of established canon?