I lived for 12 years in Texas, and all of my immediate family still live there. The fables of how Texas was formed are mostly taken as gospel, and are just as detached from reality as the zombie Jesus story.

"Stole" has connotations I wouldn't necessarily agree with. Modern-day Mexico and California were part of the Spanish Empire. Not exactly the nicest of people. "No one expects the Spanish Inquisition!" The Spaniards conquered the local indigenous tribes in the same brutal way the US did some centuries later.

The point is that when Mexico got its independence from Spain it did not return the land to the indigenous people. Like in the US, it was the Spanish decedents ruling class who took over, similar to what had happened only a few decades earlier in the US.

So when it came to Texas and California, it was one colonial power conquering another. The indigenous tribes of both countries were not benefitting no matter who won.

All that being said... You are correct that the US invaded Mexico after several years of the US arming local insurgents and using them as a cat's paw to fight the Mexican government (some things never change, eh?), and that fact is conveniently forgotten.