Good thing you IANL'd that because this is very much a state by state thing, not an "american" thing.
For example, if people openly hike through part of a private property for 5 years (in CA), and the owner knows this and does nothing, then after 5 years there will be a public easement for the public to continue using that part of the land as a hiking trail and the owner can no longer prevent that. OTOH, if he puts up signs on the 12th month of the 4th year, saying "Hiking permitted by owner", then no public easement is created, and the owner can subsequently close off public access at any point.
Every state I’ve lived in has landowner indemnification for trails. In Colorado, the landowner must put up signs for hazards, though a local group always exists to help with this. In my experience, the rationale for such a trail to be closed always comes down to a single person ruining it for everyone else.
The second you charge money (for hunting, usually), all that protection goes away.
You may be unaware, but the American legal system allows for property owners to be held civilly responsible for the actions of uninvited individuals, including criminals with intent beyond simple trepass, that harm themselves on said private property, unless the owner has taken many somewhat onerous steps to post No Trespassing signs often with requirements of details on the signs and posted in short intervals.
So why would a property owner want to allow random individuals to cross their land if it may mean someone can sue them for damages because they tripped and broke an arm, etc.?