You are incorrect. The U.S. purchased that land from Mexico for $15 million in 1848 under the Treaty of Guadalupe Hidalgo. (See my post up-thread.) The U.S. owned the land before Nevada was a territory or a state.
The phrase "extension acquired by the boundaries of the United States" means extension of its jurisdiction, not its ownership. The government does not 'own', it 'controls'. Its control is subject to the rights of citizens and inhabitants, otherwise there is no freedom.
Here's the actual Article XII from the treaty:
ARTICLE XII
In consideration of the extension acquired by the boundaries of the United States, as defined in the fifth article of the present treaty, the Government of the United States engages to pay to that of the Mexican Republic the sum of fifteen millions of dollars.
Immediately after the treaty shall have been duly ratified by the Government of the Mexican Republic, the sum of three millions of dollars shall be paid to the said Government by that of the United States, at the city of Mexico, in the gold or silver coin of Mexico The remaining twelve millions of dollars shall be paid at the same place, and in the same coin, in annual installments of three millions of dollars each, together with interest on the same at the rate of six per centum per annum. This interest shall begin to run upon the whole sum of twelve millions from the day of the ratification of the present treaty by--the Mexican Government, and the first of the installments shall be paid at the expiration of one year from the same day. Together with each annual installment, as it falls due, the whole interest accruing on such installment from the beginning shall also be paid.
Articles VIII and IX provide for protecting the 'property' and 'rights' of the inhabitants, ergo the Bundy family had grazing rights protected under the treaty. when Nevada was incorporated as a state, those grazing rights came under the state. The federal government cannot take them away unless by application of the 5th Amendment to the US Constitution.