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.