America had very little to do with Texas. Americans were allowed to settle in Texas for
very cheap and on the agreement that they farm the land. Once they crossed the border (Haha! Imagine that! Americans escaping into Mexico!), they were pretty much under Mexican jurisdiction, and on their own, granted the Mexican government was quite lenient for a while. The Texans started to demand more, and as neither the settlers nor the government would back down, the war ensued, and finally concluded at the Battle of San Jacinto and thanks to Sam Houston.

Texas, after being it's own independent republic for some time, finally requested for stateship in the U.S. Since we were our own country, and not just a territory, we were able to negotiate our terms of entry a bit more than other states. For example, the Texan and American flag may fly at equal stances. To my knowledge, all other state flags must fly in inferior positions.