States right to secede?

I’m working from memory here, but my understanding of the Texas issue is that they don’t actually have the right to secede or break up into five states (nor did they prior to Reconstruction). As I recall, Texas was an unusual situation when it joined the United States because it was a recognized sovereign nation rather than an American territory as all previous states had been when admitted (excepting the original thirteen obviously). So a committee of Texans and Americans was appointed to work out a treaty to join Texas to the US as a state. This treaty included the provisons for independance and division that people are talking about. However, before the treaty was officially ratified, the Texas legislature and American congress both passed bills declaring Texas was a state. So legally speaking, Texas became a state by legislative action and the treaty was moot.