Schools like Michigan are known to give out auto-interview invites before receiving secondaries back because they do a cursory preliminary review of primaries/recs. The prevailing theories speculate that there's a magical threshold comprised of a combination of school reputation, GPA, and MCAT.
On the other hand, there are also a few schools like Vanderbilt where you do not get the opportunity to submit a secondary until you are invited for an interview by mail.
But in all cases that I'm aware of, the schools must see your primary and maybe even letters of rec.
As for UTSW, I'm not sure what the TMDSAS process is, but for MD/PhD applicants through AMCAS, there is no secondary period.