This follows an earlier post by me on April 17 on "Who Owns Unowned Land," which argued that in the US it is the states in the original 13 colonies and the federal government in the rest of the nation, with the precise legal code defining the tenure rights being those of the nation that was ruling the land when ownership was first established. Which gets us back to this matter of how does this first ownership get established on previously "unowned land," with the implicit question for the US being, "why are not the Indian tribes the original owners?"
So, in a paper by T.W. Merrill from the Yale Law School in 2009, "Accession and Original Ownership," he addresses British common law views on how "original ownership" comes about, finding that the theory presumes that prior to individuals (or sub-national corporate entities) coming to own land, it was presumed to be "held in common," as in traditional medieval grazing commons in England that came to be enclosed, without it quite being clear who ultimately owned such grazing commons. Merrill cites John Locke on this who wrote, amazingly enough, that we should think of the world as originally "being America," that is a giant commons. For Locke it was mixing one's labor with the land that established ownership, a labor theory of ownership as it were. The matter of "accession" is posed as an alternative, but this simply involves a modification of this labor mixing principle, altering it to the first owner is the one who establishes effective control over the land. Once that is recognized, then a chain is established that simply continues, which is why we have this matter of the code holding when land first becomes clearly owned being the relevant one for later property transfers, particularly real estate ones.
Now in fact this does not really answer our question, although it does highlight important details to some extent, particularly when we consider Locke's view of "America." Why is it that the Indians did not "own" the land, or were not considered to be the owners by the British (and Spanish and French)? Needless to say, certain areas were used regularly by certain tribes, arguably enough that Locke should have granted them property rights, unless he wanted to argue that they could not due to being subhuman or something like that (am not aware of Locke ever making such arguments).
No, obviously what is involved is recognizing that behind property rights, certainly in land, there is assumed to be some sort of government or state with an organized legal code and system of courts to enforce it, even if it is one that has evolved "spontaneously" a la the common law of Britain, in contrast to the continental codes derived from Roman law, although the argument of Shleifer and his allies about the differences between these has been way overblown and often full of errors, the famous "Legal Origins" QJE paper by Glaeser and him being notorious for its myriad mistakes, even as it is one of the most heavily cited economics papers of all time.
So, private property comes into play when a government with a legal system recognizes that somebody has "mixed their labor" or otherwise assumed some recognized degree of control over some land with, very importantly, that person recognized as someone with legal rights to do so within the law code of the state involved, with that state itself ultimately having some degree of control or claim to control the land in question. This gets us back to the question of how America did not come to belong to the Indian tribes, although now reservation lands do, and many individual Indians own land privately in many places. It was simply a matter of force, although it must be recognized that none of the tribes had organized legal systems of the sort that one found in Europe. These "commons," in many cases recognized among tribes as being "territory" of one tribe or another, became the property of the relevant European-backed governmental entity that took them from the Indians, one of those acts of "primitive accumulation" of which Marx wrote at length.
In any case, in the eastern US, those entities were the individual colonies, thus allowing them to "own unowned land," with private ownership being recognized either by the Crown directly or by governors of the colonies assigned by the Crown, and the priority of their rights continuing into the independence era of the US. This also explains how certain areas that had been settled while there was French or Spanish rule with individual properties being established under their rule continued to have their tenure determined by the system of legal land tenure in place when the original ownership was established. But when the US would take control of these territories by either conquest or purchase, that land not already privately owned would belong to the US federal government, which did the conquering or purchasing, although which agency of the US government might come to have responsibility for such land would depend on acts of Congress. And, of course, the various Homestead Acts all followed the Lockean principles of mixing labor with the land to assert control and ultimately private property rights.
So, running this back to the matter of Clive Bundy in Nevada and his claim that the "sovereign" state of Nevada owns the BLM lands that he has been grazing cattle on for decades without paying any fees, his argument continues to be completely legless. If he wants to argue that somebody other than the US federal government is the owner of these lands, then the most legitimate alternative candidates would be either nearby Indian tribes (Shoshones?) or maybe the government of Mexico, from whom the lands were taken by force in the Mexican War. I am sure he does not want to recognize either of them, who would also presumably demand fees from him to graze his cattle. I know that he claims that some sort of rights were granted to one of his grandfathers, and maybe he did "mix labor" with the lands, but the courts have not recognized that claim. And the matter of him and his armed friends flying lots of American flags while denying the very existence of the US federal government at all is completely absurd.