When you’re in a hole, the first rule is to quit digging.
Here, have another
http://heartland.org/policy-documents/research-commentary-federal-ownership-public-lands
There is no doubt, the federal government owns public land, even when you write it in all caps.
By definition, public land is land within the general public domain that a government holds in trust for its citizens. The government is the caretaker of public land. Public land is different than a public enclave (which actually IS owned by government).