All land excepting the original 13 states belonged to the United States as that land was acquired. In general, the United States recognized existing private land grants and registrations in places like Louisiana, California, etc. The disposition of land was generally spelled out in the terms of admission to the Union. Texas, which entered as a sovereign nation, agreed to cede to the federal government land in what is now New Mexico, Colorado, and Kansas but kept the rest, within the current boundaries of the state.
This was not done in other states, so unallocated land is owned by the federal government. The government was initially happy to sell it, but there weren't many buyers and people freely ranged their cattle on it (the open range). Now, the government wants all people off the land, except of course, certain privileged elite, who bribe the right politician. Ranchers, in particular, are no longer welcome.
You have stated what in my mind is the case.
Apparently the law suits in the past did not properly address the issue of Nevada ownership of the land. My gut feeling is that Nevada will not claim the land and thus not vindicate Mr Bundy.
We will see.
Apparently the claims to Feds by the different states will not be the same. I thought BLM was tasked with managing all western properties not sold or rather not bought by citizens.
A case in point and strong precedent is in adjacent Utah where bubba Clinton declared Federal land under BLM control off limits for development and in effect a new very large National Park called The Grand Staircase Escalante. Unlike all other such national parks/monuments, the Grand Staircase is under management of the BLM, not the National Park Service.
The maneuver effectively removed very large coal reserves from production.