The far more likely explanation is that these people thought they were stomping on the brake, when they were in fact stomping on the accelerator. I've actually done that when the passenger kicked over a folding sun shade and it (unknown to me) wedged so that every time I pressed the brake, it also pressed the accelerator. The car would lurch forward whenever I started braking. Nothing happened because when I jammed down the brake pedal, the brake overpowered the engine and the car came to a stop. The engine was revving at an uncomfortably high RPM, but the car was stopped.
The Toyota Avensis I used to drive had some protection against this. When I pressed the accelerator pedal all the way quickly the electronic injection control would refuse to accelerate quickly instead performing a gradual acceleration. This was very annoying when I actually wanted to accelerate quickly. I had to learn to press the pedal gradually with just the right speed.