How do you know? Driver could have been looking back at his kids for all we know when the car beeped and he then paid attention.

And yes, I would say that the autopilot reacted faster than a competent human driver not expecting a crash while watching a 30 second clip. Probably by time measured in seconds.

I do agree safe following distance made the auto-breaking pretty irrelevant in this specific case as there was plenty of time for a human to react. But it's still impressive to see things working, and a bit of positive public PR hype over this tech can't be an entirely bad thing.