Let's break it down.
At 33 yards:
It takes the arrow .2 seconds to cover 100 ft at 500 fps. The first sound the deer hears is the string gate slamming down under ~200 lbs of force. That's the loudest thing on the bow, and it happens before the arrow even moves. The deer hears that sound at about the same time the arrow leaves the bow, because it takes some time for the arrow to get moving. Let's assume it's purely deer vs arrow, with the deer reacting as soon as the arrow leaves the bow. That gives the deer almost a quarter second to drop, and they can drop faster than "gravity" because they pull their legs and head up which pulls the body down. In that .2 seconds, gravity alove will have moved the deer down almost a foot, and the deer could easily double that by lifting it's head.
Here is a clip from the slow-mo guys. Take a look at the 40 second mark. The loudest sound BY FAR is the string catch slamming down. Getting the arrow moving takes a LOT longer than you think. The deer knows what's up before you even know the bow has gone off.
Can't dispute that