The issue is that though there were some settlements which one could refer to as Mexican in these territories, they like the Spanish had made very few inroads. Most settlements were along the coast in California and into what is now Texas and New Mexico. What prevented anymore then a foothold was as a result of the hostility shown both the Spaniards and later the Mexicans by the various Indian tribes (e.g. Geronimo got his moniker because he ambushed a Mexican garrison and wiped them out on St. Jerome's day). The myth, to reiterate, is the territory was sparsely populated and required American innovation and ingenuity (e.g. the five cylinder Colt revolver) in order to open it up to large settlement and civilization, though the Native American population might object to the latter.
The present descendants of these original settlements don't even refer to themselves as Mexicans. They referred to themselves, and mostly continue to as Tehanos (Texas), Spaniards (New Mexico), and Californios. Those claiming otherwise are descendants of those who migrated to the area after the Mexican American War. And they were only able to as a result of the American conquest.
So my advice to Mexico is get over it.
My cousin taught school in the New Mexico mountains and said that some of the people there spoke formal Castilian Spanish-using the vosotros form and pronouncing "z" as "th"- and had light hair, eyes, and fair skin.
As the descendents of the Conquitadors,they were rather contemptuous of Mexicans