I think the "gamey" thing has something to do with letting the blood drain. I know the worst tasting deer I have eaten have been shot during warm weather periods and then butchered very quickly. You can just see in the ground meat the blood/juice that drips out.
ryo,
When I butcher the deer myself and even sometimes when I take the deer to be butchered, I will quarter the meat and then put it in a coller full of ice and water. This gets the meat down to temp as quick as possible and it allows the blood to saok out of the meat. When I butcher myself I leave it set like that for a day or two and again I have never had a pice of "gamey" meat with this method.