this is very common in the west. Its one of several ways to "own" more property than you paid for. If your property completely encloses 1000 acres of public land, that land is as good as yours (with the exception of building things, but many of the property owners in these cases are taking people hunting on the land, so no permanant structures would be built anyway.) Another common thing is land leases. I don't know…
If it doesn't grant them exclusive rights, and they can't e.g. put up "no trespassing" signs, wouldn't that be a crime because they are claiming ownership, and thereby claiming that the state does not have ownership? Have you ever reported one of them to see what happens?
Sadly today too much of the law is political, both left and right, with police and prosecutors choosing what laws they want to enforce, when, and on who (i.e picking people or groups they dislike)