Here's the exact wording from
TMDSAS:
"Applicants may hold offers from one of the TMDSAS medical schools as well as other non-TMDSAS schools such as Baylor College of Medicine. By May 15 of the matriculation year (April 15 for schools whose first day of class is on or before July 30), each applicant who has received an offer of acceptance from more than one school must choose the specific school at which the applicant prefers to enroll and withdraw his or her application from all other schools from which acceptance offers have been received.
After June 1, no medical school in Texas may offer a position to an applicant already accepted by another medical school in Texas. This is the result of an agreement between the four UT System Medical schools, Baylor College of Medicine, Texas A&M Health Science Center College of Medicine, Texas Tech University Health Sciences Center School of Medicine, and University of North Texas Health Science Center at Fort Worth College of Osteopathic Medicine."