(Apparently the Rimac Nevera, with about 2000hp, can accelerate faster than it brakes. So that one might be the only exception. So unless you're driving a 2000hp car, the brakes will always overpower the engine, that is not debatable.)
Brake fade is irrelevant here. Brakes fade when overheated beyond their operating range, either due to fluid boiling and/or the pads overheating. This is nearly impossible to achieve in street driving, but can be experienced on the race track. None of the claimed acceleration accidents involved extreme repeated braking prior to the incident.
This "scandal" was never about mechanical failures. It was almost certainly about driver error and mass hysteria.
As for Toyota settling, had this been Ford or Chevy, the government wouldn't have had the appetite to go after them for what was always a non-issue. It was just less expensive for Toyota to fix floor mats and pay a billion to put it all behind them.
I don't know enough about 2005 Camry's though, so I wouldn't speculate much further than that.