There is not too much time to react when the car starts unexpectedly speeding all of the sudden.

True.. but this guy was a cop.. supposedly an expert on safety..

Brakes will stop the vehicle, but you have to commit to stopping the car as opposed to using the brakes to just prevent the car from speeding. If you just use the brakes to keep the car from speeding, you’ll overheat them because the brakes will not be able to cool down. As you mentioned neutral works.. and so does off with the Start/Stop button.

There is also not much time to react when something happens on the road in front of a driver. I think the real thing that happened is that this driver panicked.