What's funny is Mexicans saying the Southwest US is their rightful homeland. Nothing could be further from the truth.
Mexico became independent from Spain in 1821 and claimed the Southwestern US for itself for 14 years until 1835, when Texas gained independence from Mexico. By 1847, the US claimed all the territory to California after the Mexican-American War.
So, California was a Mexican territory for 26 years right after Mexico became a nation. Mexico couldn't hold it as a territory, and no Mexicans lived there except in a couple missionary churches. The US gained independence from Great Britain nearly 50 years before Mexico gained Independence from Spain. The US acquired the Louisiana purchase from France while Mexico was still a territory of Spain.
The Mexican people themselves are descendants from Spain (all but 5% of the indigenous population was killed off by small pox).
If anything, the Hopi, Navajo, and Apache have claim over the Southwestern US. Not descendants of Spanish immigrants who have never lived there.