Usage of "the" before university subdivision names.

Hey y'all, I'm actually a native speaker but I have a question that I can't find a good answer for, and since so many grammar gurus lurk here I thought it'd be a good place to ask. I believe something like it has come up here before, but my specific query has not. I know you should put a definite article before a university's name if the name is like "University of Texas" but not before "Texas University," e.g., "It is the policy of the University of Texas" vs. "It is the policy of Texas University." (I'm just using Texas here as an example.)

My question is if you need an article when describing a college or school within the university if the name of the university is [insert name here] University. For example, Texas University School of Medicine. IMO, "It is the policy of the Texas University School of Medicine" sounds better than "It is the policy of Texas University School of Medicine," even though you shouldn't use an article for "Texas University." I also believe that "It is the policy of TUSM" would leave the article out as well. Thoughts?