I've seen slow-motion video and the deer do drop and drop fast when they hear or sense something is not right. It looks like they are pulling themselves down.
And they will often do exactly that. Have seen it many times.
That is why shooting a deer with a bow should only be done at bow range.
IMO, start throwing arrows/bolts out 40-60yds and jumping string really comes into play.
The chance of a deer 'jumping string' at 10-30' with the speeds of todays bows with a well aimed, broadside, centered heart lung shot and the arrow landing clear out of the kill zone or even missing the deer completely would seem to be rare.
I can only think of a few times that I let an arrow fly just as the deer suddenly moved. It does happen. A deer turning, taking that sudden unexpected step at the very time my mind says shoot. But these were not cases of the deer moving due to hearing me. Just bad timing.
But all other bad hits have been due to error of some sort on my part. Error in pin usage, error in shooting judgment when shooting uphill/downhill or just simply pulling off. And lets not even talk about that small twig I didn't even see cause I had such tunnel vision on that sweat spot.
But hey, it would make me feel better if I could blame these errors on the deer.