Seems like the reasonable thing to do to protect yourself from liability would be to give up a tiny strip of your land that provides public access to the publicly owned land. That way people who want to go to the publicly owned land go on that path and don't come on to your property and give you all that liability. It'd be a teeny fraction of land, but you could say with a straight face, "Hey, you wanted access to the public land? Use the nice convenient wide open access point, as the clearly posted signs indicate."

Intentionally buying up land that perfectly surrounds public land on all sides really betrays what's actually going on here.