I get that; my point was that if she does research in any sort of academic setting, you might be able to work with her. If it was a private setting, you would definitely be out. But since she works in an academic setting (at least that's what I get from what you've said so far) the only way that you can know whether she would be open to you doing research with her is to ask. Maybe it will be a problem that you don't go to the university that she does research at, and maybe it won't. You won't know unless you ask her.
On another note, it really sounds to me like you are trying to talk yourself out of this. If you want to do research, and have an avenue that is possibly open to you, why are you not pursuing it? The worst case scenario here is that she says no. It's not like she'll be really angry with you for asking a simple question like this.
Edit: If your confusion is coming from the fact that UT Southwestern is an academic medical center not affiliated with an undergraduate institution, that's understandable. However, there are students of some sort trained there which makes it a for-sure academic setting. They might not have a habit of taking undergrads in, but you won't know until you ask.