Mexico didn’t get formal independence from Spain until 1821. And the first few Americans invited to Texas were invited by the Spanish, not independent Mexico.
My contention is Texas was NEVER Mexican, it was part of the Spanish Empire, but not Mexico after independence.
From Wikipedia:
After receiving a land grant from the Spanish Crown in 1820, Moses Austin planned to be the first to establish an Anglo-American settlement in Spanish Texas, but he died before his dream was realized. On his deathbed, he pleaded with his son to fulfill his dream to colonize Texas. Stephen led the colony to a now-sovereign Mexico in 1825, and in time, the settlers demanded autonomy and later won independence from Mexico under President Antonio López de Santa Anna, thereby establishing the Republic of Texas.