Poser, thinking about it some more, I wouldn't be surprised if that guy was bragging, doing some chest thumping without realizing he was just making a fool of himself.
East TN hunters are probably more likely to quarter than drag given the terrain. Another reason Western hunters quarter (and not just elk, but mulies, white tails, antelope, etc.) is all distances are just much greater out west. When I've elk and mule deer hunted, the trail head is at 6,000 feet, ride the horse 9 hours over the 10,000 foot pass, down to make camp at 8,000 feet and hunt between there and 10,000 feet. Wiser to quarter and haul the meat in saddle bags (or your pack if on foot) than drag a deer even a short distance in grizzly country. Don't have ol' grizz around here. Couple that with many places out West don't allow vehicles.
In addition to being better for your back and heart, I think quartering must be better for the meat quality. I'm surprised that some don't even field dress. I guess if you are only hunting mature bucks or don't like venison and will donate to HftH, that makes sense. Who wants that tough old meat. But a doe, I want to get her dressed right away. To me, quartering will just get that good venison cooled down that much quicker. Further, many aren't going to do their own processing so quartering to them doesn't make any sense if they aren't going to skin and butcher the deer themselves in any event.
To each his or her own and if it's a short drag I might. Still, if it's rugged terrain (and that includes logs, rocks, ditches, creeks, thick/thorny stuff, not just mountains) a long drag (say more than 1/4 mile, maybe even a shorter distance), then I'm quartering.