Can't say I've heard stories similar to those, ..., but ...,
I have heard fellows who claimed that anything less than a .338 Winchester Magnum would not down a whitetail, or at least not well, and when using less the hunter was doomed to a very long and likely unsuccessful tracking situation.
The truth was more akin to a situation where the hunters were poor marksmen, and were depending on massive impact damage from the bullet to make up for the poorly placed shot.
I have been told that a pure lead, patched round ball from a muzzleloader could not hit a deer past 50 yards, let alone kill a deer beyond 50 yards,
My farthest harvest of a whitetail was at 110 yards with a .530 diameter round ball, all lead. The deer moved 20 yards from where it was hit.
I was told by a hunter that had practiced well with his rifle, and because he was hunting in a very brushy area, he had been using a lever-action in .44 magnum. He had shot at a deer at around 50 yards and was amazed that he had missed, as he could not find it, nor any blood, and wanted some help just to be sure....,
...,When I got out to the property about 4 hours had elapsed from the shot, but he was very sure he had an accurate rifle and it was a 50 yard shot..., he had stomped around for a couple hours moving farther and farther away from where the deer had been standing, but found no sign. We went back and started from where the deer had been standing..., we found it about 40 yards from where he had hit it. The whitetail had moved downhill a short distance and then crawled under some thorn bushes to hide, and had died. He had walked past it a few times; never saw it. No blood on the ground but a bunch about 2 feet above the ground on the brush, as the animal had coughed a lot as it moved. Lack of knowledge of where the blood might be, the behavior of injured deer, and lack of confidence in what his rifle would do, were the key.
I can't say..., that I have always been without mistakes when looking for downed deer. I learned to look at the ground AND to look a foot or two up on the brush, because I looked for a downed deer, found no blood on the "ground", and after an hour went back to "start from the top" from where I was sure I'd hit the deer..., and the second time I noticed the blood. I was rather embarrassed when I saw how much blood I had completely overlooked, by having too much tunnel vision.
LD