Big disclaimer: I know nothing about the rules of applying to Texas medical schools.
That being said, it seems to me that you wrote a letter saying, "I’ll go there if you accept me." This was an offer by you.
They did not accept you. Your offer was rejected.
There was no offer and acceptance. There was no contract. There was no implicit or explicit agreement. There was no meeting of the minds.
It’s kind of like when you apply ED to undergrad and get deferred. After the deferral, you are no longer bound to go there even if you subsequently get in.
So, I would be completely shocked if you are ethically, morally, and forget about legally bound by a letter of intent sent prior to decision only to have been placed on the waitlist.
Of course, if you send one now knowing you are on the waitlist that’s a completely different story. But other than that, they are out of their minds if they think they can enforce a pre-decision letter of intent that did not result in a decision of admission.
This is the advice of someone who knows nothing so take it for what it is worth—nothing!!
Best of luck!!