Thoughts of a former Range Master.
:sniper: As a former Navy Range Master (M14 Rifle, M16 Rifle, 12 gauge Shotgun, 45 cal Pistol, 38 cal Revolver and other personal small arms qualifier - Urban small arms tactics and Field fire and maneuver small arms tactics instructor), I believe that I can shed a little light on your conundrum.
Snipers are trained to fire at the "belt buckle" portion of a long range target because it is considered to be the center of the "bottle" portion of the target or as it is sometimes referred to as "center mass". It is easier to have a hit at long range by shooting center mass than any other portion of the anatomy. Snipers are not always trained for a clear kill, rather they are trained for a shot that will remove the target from being a viable threat and causes 2-3 other people to be tied down caring for the wounded soldier. Real "head" hunting is unusual and is used in only the most limited way - the target MUST be of "high" interest and there must be no other way to cancel out his/her influence.
Many years of refinement have proven that with consistent usage, center mass firing at long range improves the "kill" ratio of the average foot slogger or for a matter of course - any person in a combat role using a long rifle no matter the caliber.
One of the things that snipers learn through trial and error, is that by using the center mass targeting it does away with some of the missed shots caused by someone moving their head. It's only in the movies that Mr "Vonderzhooter" is able to take the iris out of an eye at a thousand yards. Most long shots are in the 750 yard or less ranges with the majority being less than 500 yards. The one sniper range that I am familiar with has targets that start at 100 yards and go out to 1000 yards. I don't know what the ranges are for all firing ranges.
As to whether a "deer" hunter is a really better shot when it comes to sniping, I don't believe that one really tracks. Being a "nature" freak does help with the sniper's ability to blend into his environment better than a "city slicker" who has never been in the wilds. It does not have anything to do with the "natural ability" of expert riflemen and snipers. There is a feeling to the aura of a grove of wild forest that can be sensed if you are aware of it that can be very valuable if you are hunting another man. The aura is different when man has not intruded his presence to where it is noticed by the animal life that makes the forest their home. That change "can" tell you whether you are alone or if someone else is there. It can make the difference between life and death for the dedicated sniper.
I don't know if this helps but it was something that didn't appear any of you had considered.