Mexico "administered" California for less than 40 years, until the Bear Flag Revolt that occurred less than 20 miles from me. Mexico could have stomped it out, but at that time California was considered by them an undesirable no man's land.
Mexicans only want to take over areas already made inhabitable by others. Do you see them out in the middle of the Mojave Desert demanding that that land be returned?
Not to mention some of my state's original inhabitants like the Chumash, who might have a small problem with Mexico claiming this property as rightfully theirs.
If we are going backwards in history to determine ownership rights, they win hands down.