If the frame failed upon a hard acceleration, given that everything appeared fine up until it happened, then should this not be covered under warranty? Otherwise, how can anyone ever get their warranty honored? The company can just claim, "Oh, well you must have dropped/crashed the bike on some previous occasion thereby compromising its structural integrity".

I suspect the denial of the claim has nothing to do with FUJI believing the frame was dropped or knocked up. Rather, the location of the break is typical of a misadjusted RD that is shifted into the wheel and thus they assume this is what happened. If the break had occurred anywhere else in the frame I'm sure they would not question the OP's claims. However, based on the OP's own account this is almost certainly NOT what happened (unless OP is mistaken about which direction he shifted in, and even then there would be some fault with Performance's RD adjustment).

So, is the derailleur hanger/dropout a possible point of fatigue/failure on a frame and with what likelihood? Second, although the OP claims the QR was tight, could the failure have been in the QR skewer rather than the frame or derailleur settings?