>> “ The BLM, or rather the various agencies it is descended from, go back to before the Constitution” <<
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That is gibberish!
Do you have the slightest idea when the US gained title to Nevada, and the conditions under which it did so?
All private land claims take precedence in these purchases, so the BLM or it’s predecessor have the weakest of all claims to any particular parcel.
The State of Nevada owned the land before the Bundy family began using the land.
The Bundy family never met the requirements of color of title, hostile possession, or payment of taxes to gain title to the land, and grazed cattle there with permission from the state, and later, the BLM. Nevada law specifically provides that making improves to land does not confer ownership.
The Bundy family has never contested ownership of the land. He admits that. In fact, they've confirmed ownership by another party by entering into contracts to use the land for grazing cattle and by paying a fee to do so.
Twenty years ago, Bundy didn't like the terms of the new contract presented to him, so he refused to sign it and quit paying grazing fees. He's been ordered to pay grazing fees multiple times over the last twenty years. He's ignored those orders. The last order gave him 45 days to remove his cattle or else they would be treated as trespassing cattle. He never attempted to remove his cattle.
Uhh, yes I do.
Nevada, or at least the vast majority of it, was ceded by Mexico in the Treaty of Guadelupe Hidalgo of 1848, which closed out the Mexican War.
Land grants from the period of Spanish and Mexican control were supposed to be honored, but weren't always.
Federal title to unclaimed land did not originate with the BLM. That agency was established to control land already in federal possession and not previously assigned to another agency such as the National Park or National Forest services.