I've done alot of group hunt firearm deer drives. I've seen too many deer harvested from a running shot, to belive it isnt going to happen with one shot. Thats even in shotgun only states, not to mention rifles. I even harvested a buck with my bow, as he was striding through my shooting lane. If didnt take the shot he would have walked out of my life forever, but I put it on his shoulder and double lunged him at 35 yards. I wouldn't recommend shooting your bow at a running deer though. If your weapon skills arent up to performing walking or running shots, then no you shouldnt take a shot like that. But if you can shoot doves flying in over a pond, rabbits running,or quail flying, etc. You can lead your game, and you can shoot walking or running deer in the vitals. Don't mistake my skills as reckless abandonment, I aim at what I shoot. I dont condone shots at the deers rump at anytime, you won't usualy retrieve the deer when you shoot them there. Only a fool would take just one bullet to hunt deer, and the thought of that is more un-ethical than any kill shot at a running deer will ever be. Like it or not,there are many hunters that have the skill it takes to harvest moving game.
"Let a young buck go, so he can grow."