My experience, hair will not taint deer, elk, or moose meat, and I didn't notice any ill effects with bighorn sheep or Mt. goat either. So, MYTH.
However, FACT, pronghorn antelope hair has very strongly scented and flavored oil, and will impart a taste most people don't like to meat. So with antelope, it is pretty imperative to keep the hair off the meat, and if there is any contact remove the hair ASAP. Antelope are very different than other big game, hanging ruins the meat (unless you love steaks with the consistency of liverwurst), it is just ultra-delicate compared to the deer and bovine families. I believe this is why so many people, including experienced deer and elk hunters, "don't like" antelope - they inadvertently ruin the meat with care that would be just fine for deer and elk. Quickly killed, skinned, boned out, kept clean and immediately chilled, pronghorn is the finest meat around.
Got a bit off subject there, but hopefully that little manifesto will help someone out in the future. I've eaten over 70 pronghorn, and the two that were bad, were REAL BAD, and had to do with the care received.