You can see that in West Florida, the Louisiana Purchase, and later acquisition of the PAC NW.
Mexicans sought to obtain those same territories themselves and looked on the efforts by Spaniards to become part of the United States as treachery.
I think the Spaniards were correct, and as a consequence the Mexicans have no legitimate right to be here under any guise ~ not even as tourists. That war ain't over ~ and most Americans don't even realize it has been underway for nearly two centuries.
You're correct about the original relationship being between Spain and the U.S., not Mexico and the U.S.
Mexicans who complain about U.S. social attitudes are really cruising for a bruising -- Mexico revolted against Spain because of new Spanish laws liberalizing the old social rules, lessening the social distance between proud, stuffy, racist criollos (Creoles) like, oh, Presidente General Antonio Lopez de Santa Anna, on the one hand, and humble mestizo Mexicans on the other. So Mexican independence was actually founded on Creole ethnic and social pride -- no kidding!
But the original deal the U.S.-born empresarios had was with the King of Spain. In fact, Moses and Stephen F. Austin were both Spanish subjects when they lived in Missouri, and they were granted commissions by Spanish officials to carry out a Roman-style scheme of Anglo-American settlement in Texas (think, back-fire break) under the protection first of the King, and then, after the Spanish were sent home, under that of the Mexican Constitution of 1824. The idea was, orderly settlement and pledges of loyalty under Spanish law, to prevent a disorderly mass invasion and total loss of control. Guess who broke that deal? Gringo-hating Santa Anna, that's who.