I don't at all doubt what's been said above; I haven't lived in Montana very long. One thing I suspect, though, is that elk are changing again. When Lewis and Clark came through, elk were mostly a prairie critter. Hunting pressure made them move to the mountains.
An elk can live in the Bob Marshall Wilderness, no doubt about that. However, that elk has to scrape by on whatever happens to be growing up there, and then move somewhere lower for the winter. Nowadays there are wolves in there, so that same elk has to spend a lot of time watching for them. An elk on private land has less pressure, and can winter on irrigated alfalfa. Which of those two elk are more likely to make it through the winter in good shape?
Elk don't know when hunting seasons are, but they do avoid people. Wolves also avoid people, so there are more of them in wilderness areas. When an elk is bumped, by people or wolves, he moves. If he moves within public land, he gets bumped again. If he moves into private, he is pretty much left alone, so he stays there. Next year he may go back onto public, or he may decide he has everything he needs on private. If he does go back to public, the same process repeats, and I suspect he is less likely to leave the private the following year. He has no idea it is private land, he just doesn't have a reason to leave. Meanwhile, the wolves in the wilderness areas have less elk to hunt (and deer, by the same process), so each remaining wilderness elk gets bumped more often by wolves. And none of this takes mortality into account. Many, many more hunters are on public land than private. The current trend is for relatively wealthy hunters to hunt every state they can, which crowds things even more. So the decreasing public land elk population gets hit harder during hunting seasons. Ranchers don't like wolves, so there are more wolves on public land too. Managing elk by hunting unit does not take into account the disparity between private and public lands. FWP count elk within the unit. They need to manage all the elk, and the only tool they have is hunting licenses. They can't do anything about the elk on private land. The only thing they can do is try to kill off enough elk so the private land elk will move out to the less crowded public land. It is far from ideal, of course, but as long as there are vast private land preserves, public land hunting will struggle. And as long as there is big money to be made in outfitting, the problem will only get worse.