Easy to say watching the videoBeing in the middle of something like that is an entirely different story. I'm sure his brain was like "whaaaaaaa...." when his brake pedal sank to the floor. By the time his brain caught up with the situation, he was already through the gate. Trust me, unless you have a good amount of experience and/or are really quick-witted (or perhaps just lucky), that kind of stuff happens in a heartbeat and it's hard to always "do the right thing."
That's what I was going to ad as well. You're literally waiting to hit the brakes at the very last second, so you're on the throttle until that point. And if something goes drastically wrong you're scrambling to get the car stopped. Not sure what the driver's experience level is, in my experience the brakes show you signs that they are getting heated that you feel in the 2 or so corners before this happens. That's your sign to expect something and have an exit strategy. Also need to consider lap traffic behind you to make sure you and others are safe, so shutting off the ignition while on track could cause a huge incident.
