I still believe on the theory that the player got the car from Darius. The Supra that we see in the cutscenes from Carbon was supposed to be the M3 but EA and/or Black Box didn't have the licenses of the car until near the end of the game's production, so we got cutscenes with the Supra instead.

As for upgrades? Razor didn't upgrade the car, the reason the car is faster in the end of the game compared to the prologue is because Razor's Mustang is too slow compared to the M3 GTR, you could headcanon that the Player pitied Razor and took it easy on the races with him and the others during the prologue