Something similar having happened to me, my personal story can perhaps provide one data point. This goes back about 20 years, but I believe I was driving a Pontiac station wagon (ironically, I also had a Toyota Corolla at the time....). I was driving along a somewhat curvy road at about 45mph, when the car started accelerating greatly. Although I repeatedly lifted my foot and tried to hit the brakes, the brakes did not seem willing to depress and the car kept accelerating.. It seemed within moments I was over 60mph, and my heart was about to burst through my chest. Then, for no apparent reason, the auto-acceleration seemed to disappear and the car was back in my control....
It has always been my hypothesis that the floor mat had became entangled with the accelerator AND possibly the brake as well. This could explain why the hitting the brake did not seem to function as expected. As it is, I could never tell that this was the case, because the car's jump in speed happened so quickly that I had no time/capability of looking down during the incident. Afterward, the mat was in a forward position, but I can't say for sure that it was the cause.
My one regret (shame?) is that I didn't think fast enough to try putting the car into neutral or pulling the key. We should really train new drivers to think about what they would do in these and related situations (e.g., if the brakes fail -- try emergency brake, low gear, etc.)