The story is mostly true, but the parts that are not make all the difference. The federal government owned all of the land comprising the the Nevada Territory excepting that in private hands through Spanish grants and those lands disposed of by the federal government prior to statehood.
Most of the states, particularly those in the West ceded some of the land within their boundaries to the Federal government as a condition of joining the union. They did this to avoid debts that would have been incurred as a condition of statehood. In turn, the Federal government ceded back to the states certain land to support schools and state level institutions like prisons, colleges, and the state capital.
Nevada was no different in this regard excepting that so little of the state was in private hands. As pointed out in the article, the population was only 40,000 and very little of the land had been apportioned through Spanish grants.
The policy of the federal government was to dispose of this public lands to raise funds against the public debt and to reward soldiers for their service. After the Civil War, they needed to do both. Unfortunately, Nevada land was not primie quality and the laws limited the size of grants and sales. The land didn’t move and the federal government was stuck with it.
What they did was legal and it is how the federal government came to hold title to so much land. Certainly, the federal government could have fixed that, but in 1976, with the passage of the Federal Land Policy and Management Act, the official policy of the federal government was changed to cease disposing of public property and to begin to manage the land for “multi-use+. Multi-use has turned out to favor the enviro wackos and the corrupt friends of Democrats.
The notion that the land is owned by someone else is sheer nonsense.
You are right....there are reasons so much of the land in western states are owned by the feds.