I'm no auto expert, but the stories don't seem credible. Braking systems are more powerful than engines so functioning brakes can stop an accelerating car; if the stories are true, then the accelerator and brakes failed at the same time - and then miraculously went back to normal. That seems impossible even with the computer malfunction explanation.
The most plausible explanation is that the drivers panicked and hit the accelerator when they thought they were braking. The more they tried to brake, the faster they went - because they were pressing the accelerator, not the brake. The panic explanation is reinforced by other things in their stories: they always seem to keep accelerating without thinking to put the car in neutral and turn it off.
This is is what I think happened: there was a problem with Toyota floor mats (the original issue) affecting the gas pedal, after which Toyota drivers with this sort of driving mistake in their past started re-remembering their mistake as a fault of the car. That whipped up a mass hysteria. And perhaps Americans who fear for their domestic car industry were happy to feed the scandal.
People who believe that Toyota has a zillion defective cars should take a look at the runaway Audi scandal of 1986. This sort of faux scandal has happened before.
Me, I drive a 13 year old Corolla that has cost me virtually nothing in repairs, and when it gives up the ghost I plan to get a Yaris. There might be some good bargains on used ones...