The states of the Southwest were in turn created by the Federal Government, and took the lands in question from the Indians, who had no concept of land ownership, only tribal territorial rights. Still, in the case of Utah I recall a crooked deal between the Clintons and the Riadhi family of Indonesia, which helped the latter corner the market on low-sulfur coal.
Title to land in states of what is now the Southwest was legally held by Spain and then Mexico. Some of it was handed out to favorites by these governments in land grants.
Title to all of of it that wasn’t granted passed to the the United States government by the Treaty of Guadelupe Hidalgo.
Tribes are considered to have aboriginal title, a sort of inferior title not including full sovereignty. Dealing with Indian tribes has always been considered to be exclusive to the federal government.