Back in the very early 60's a buddy and I were running our beagles on cottontails. He was carrying a High Standard .22LR which he would shoot to encourage the hounds. While trying to get ahead of the dogs he flushed a pheasant which he proceeded to take out of the air with one shot. Uncertain whether he was legally allowed to carry the pistol for this purpose (this is Canada remember). Not that it matters anymore as he has now passed on to the Happy Hunting Grounds.
My buddy was probably the best all around shot with all types of firearms that I knew. I always took it as a matter of skill and not luck. Another time we were out hunting and a jack rabbit jumped out in front of us. Before I could even find the rabbit in my scope he shot and hit the rabbit in the back of the head, centred between the ears. I never questioned his ability.

Jim