True.
Nonetheless, you attributed two serious errors to the slide show you saw in St Louis, in addition to omitting a rather important fact that's highly relevant here: Years after Mexico had declared its independence from Spain, but shortly before that independence had been achieved, Moses Austin negotiated a land grant with the Spanish governor of Mexico that called for a settlement of 300 immigrant families. Moses Austin died soon thereafter, and the settlement was accomplished by his son, Stephen F Austin, during the years after Mexico had achieved its independence. Austin and his settlers maintained generally good relations with the government of newly independent Mexico, which of course included Texas at that time, leading to more immigration of English-speaking settlers into Texas. Conflicts eventually arose, including a conflict over the settlers' importation of slaves, leading Austin to support Santa Anna's rise to power. Mexico eventually feared the United States might attempt to annex Texas; in 1832 the English-speaking settlers of Texas held a convention designed to reaffirm their loyalty to Mexico while requesting reforms such as a return to less restrictive immigration policy and a greater degree of influence within, or some degree of independence from, Coahuila y Tejas (which included Mexican Texas).