I concur with your theory. I'm a firm believer that adrenaline does taint the meat. You must kill the deer in such a manner that it is not "spooked" by the act of an arrow passing through it. Sure, it feels discomfort and is quite surprised; as long as the deer doesn't associate YOU with the discomfort, it won't squirt those adrenal fluids into it's bloodstream; destined for the muscles that we eat.

Kindest regards,

-Will in Maryland