A lease is a contract and you had better read it carefully. Around here a hunting lease is a contract with a private land owner and in effect all wild game is your property. Though you are regulated by a government agency.
Most of the problems I've had are with ranchers who lease the grazing rights from BLM, the State or some other government entity and think they own the land and everything on it.
Or somebody who owns a tract of land across the mouth of a canyon and claims the whole canyon. I've seen people do that, who own the entrance point and in effect control (claim) hundreds of square miles that aren't theirs to control.
I've been sited for trespass half a dozen times and maybe once they were right. I've even been sited for trespass on private property with written permission from the owner to be there. I rarely fight it, it is easier to pay than fight. Usually a $15-$20 fine, cheaper than taking the time off work to fight it. My guess is the local Cops have some sort of understanding with the locals to run off the riffraff.
My way is to make sure I know where I am, so if it turns really ugly, I'm right and they are wrong.