Public land is just that - public. It is NOT the state's private property. The state is not a private property owner, and has no authority to act as such.
That's right. Public land belongs to the state. The state is the public. We people are private citizens. Maybe it's different in a commonwealth, probably even clearer. A private citizen has only the enumerated rights once he is off his own property, and even there he is not perfectly free to do anything he wants. Driving is a privilege, as they say, but walking on the public road is also a privilege. The government can order you off the street at any time because they own it and you don't.