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Your total lack of understanding of land rights is glaring!
If you look at the maps of the public surveys of that land you might start to understand.
The only land that the Feds surveyed in the 19th century was the unclaimed lands. That amounted mostly to that which was too steep or rocky for ranching.
Changing the governance from Spain or Mexico to the US didn’t effect ownership of grazable or arable lands.
This is my business and profession; I deal with it daily.
The US government is 100% wrong every time in the West.
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The chain of title matters, but Spain or Mexico has no claim. The Bundys likely do however.