I dont agree that a thumb shot with a 22 (or anything else) should qualify as a one shot stop. For the intent of the concept, it doesnt equate. Yes, I agree the concept is complicated, and clouded with the past theories/"tests"/debates, but its still a fair question. What works consistantly well?
The other aspect mentioned, a good hit with a 22 will "kill", whereas a poor hit with a 44 won't doesn't add anything usefull to the discussion. The difference between kill and stop are vast. I may be able to kill a deer with a 22 shot to the body, but it means little if I want to eat that deer, it wont likely succumb in any time frame thats going to do me much good, same with defensive use of some calibers. Yes, some smallish calibers are better than a sharp stick or harsh words, but many things will work much better, and predictably so. Dont shoot poorly with the 44, and it changes the picture entirely. That's a predictable result also. Shoot well. I'm not sure why it seems to be supposed that a larger caliber will be shot poorly in those comments.
There's no magic bullet or caliber. Some seem to work better than others on a consistant basis, some less so. Looking at the question is interesting, and can yield useful information. Still, no guarantees on exactly whats going to happen every single time. Kill enough critters, and that lesson is reinforced over time. Everyone wants definitive results. Life just isn't like that.
My default assumption isn't "they'll probably run off if they get shot or shot at", its more like the deer, "they're going to try their dead level best to do whatever thay had in mind when this started, or will take this very personal and aren't giving up easily". If it goes the other way, OK, if it goes the way I think it may, I don't want to handicap myself right from the start with the smallest gun I can carry.
