Article 4 sec 3 of the constitution gives control of land to the United States and empowers Congress to regulate and dispose of them. The United States is we the people and our elected representatives as guaranteed by the same Constitution ie a Republic form of government.
The Federal government is a separate entity. It is mearly the embodied branches of government at the national level. It is not the United States.
Article I Section 8, clause 17 of the United States Constitution is specific.
Therefore the Federal Government does not "Own" the land with exception of DC and needful buildings such as military, docks and the like. It is specifically delineated.
Amendment 10 specifies all power not specifically given to the federal government is retained by the states and or the people.
The fact that government exceeded its mandate during the expansion west does not legitimize it.