I am going to take a little different track than is traditional on this question. I believe that sometimes we assume that we know why something works better, and if it does, that mistake is not critical. Yes, sleeving an action makes it stiffer, but I do not think that is the main reason that it helps factory actions as much as it does. I believe that the primary advantage lies in the great increase in bedding area, particularly when not glued in.
Back when I used to do some magazine writing, I had a chance to have a Remington action, that wears a tight necked .222 Hart barrel, sleeved. While I was pondering this option, I asked a well known smith and competitor, (who had built his own line of actions, and I believe may have made the record book), if there was any advantage to sleeving a 700 if the alternative was gluing it in a modern fiberglass and carbon fiber benchrest stock. He told me that there was not, and I believe that he is right.
Further reinforcing this idea, I was lucky enough to have Kelly McMillan give me one of his prototype Edge stocks, installed on the barreled action that I mentioned above. He asked me if I wanted it pillared, or glued, and I decided that given his gunsmith's likely expertise, that it would be a good time to try a glue in, something that not been adventurous enough to try on my own, because of the need to drill accurately located trigger pin holes in the stock.
I had shot that setup pillar bedded for a long time, and knew pretty much what it would do, and after it was glued in the new stock, it took a noticeable step up in accuracy, venturing into the teens, having been previously stuck in the low twos. I realize that there are other factors involved, but all in all, I still believe that gluing in the old 722 was as good of a boost as if I had had it sleeved.
On the other side of the coin, I have a friend that has a rifle that has a Sleeved 700, that is pillar bedded into a older style McMillan stock, and he always remarks as to how consistently good its accuracy is. He does his own work, and has several other rifles that shoot well, but are not as day in and day out consistent.
I have seen sleeved actions win against custom actions, and not that many years ago, so I would never discount the potential of a sleeved action that had been completely gone through by a top smith.