Yes there might be a rule stating that tree stands become public property but where the heck are your ethics?
Public land is public land....including stands. I would never take a stand belonging to someone else, but if I found a stand....I sure as heck would hunt out of it if I wanted to and the guy wasn't there.
Simply put.....you can't put up 25 stands locking up an area to yourself. IT'S PUBLIC LAND! This is the exact reason why I think on public land, you should NOT be able to leave stands up overnight. Start everyday with a fresh slate.....first come, first serve.