Wilbur,
I have had one of those rifles that had butt jumping issues, and I came to the conclusion that it was happening after the bullet left the barrel. Just like your friend's my groups gave no indication that it happened. My guess as to what caused the problem is too far off topic for this thread. On the matter of how one shoots mattering, I have done a lot of experimenting, at the end of shooting sessions, after establishing that the load was in tune, and that the rifle was performing well shooting free recoil. IMO while there are a variety of methods that will work, one can also degrade performance by the manner in which a rifle is shot. On the pinning thing, I remember reading an article on 6mmBR,com about a successful short ranger shooter (you would know of, but whose name I cannot remember just now) who shoots that way. I tried it, and did not find it to be an advantage, but I do believe that it has some potential when used with a stock and rest setup that does not track consistently, or has a deficiency that the additional damping helps. Related to this, years back I was shooting one of the thin folded bag Hoehn tops and decided to add sand to the front bag to improve tracking. It did, but along with that came an unacceptable amount of vertical. I decided that since there was no tracking trophy, that I could live with the additional re-aiming, and removed the sand that I had added. No less of a notable than Warren Page cautioned against shooting heavy recoiling hunting rifles off of hard front bags. I have friends who prefer Bulls bags for their hunting rifles even though they have more conventional front rests that they use for their varmint rifles, so I would say that their preferences definitely follow Page's recommendation. Overall, I think that the best advice is to try a variety of equipment for each rifle, as well as shooting techniques, and let it tell you what it prefers.