Last :32 seconds of a game...who decided this one?

I think the argument is about him moving faster, you are assuming he is reacting to the snap, he is simply guessing (thats why they were offsides multiple times). 

So the defensive team could argue they just guessed right, did not react to stimulus rather guessed at the right time. They are allowed to guess. But I think it would be physically impossible, even if a player guessed at the precise moment, for a defensive player to swipe their arm into the neutral zone and hit the ball before it got to the QB (unless he was offsides).

Regardless, I do not believe that a defensive player can touch the snap before it touches an offensive player or the ground. I believe the illegal snap rule is defined as the following:

Snap fails to immediately leave the hand(s) of the snapper and touch a back or
touch the ground.

In other words the defensive team cannot tough the ball, following the snap, unless it hits the ground or an offensive player first.