Tex. Ins. Code § 601.004

This chapter does not affect the authority of the department or another state agency to adopt stricter rules governing the treatment of health information by a covered entity if another law gives the department or agency that authority, including a law or rule of this state related to the privacy of individually identifiable health information under Subtitle F, Title II, Health Insurance Portability and Accountability Act of 1996 (42 U.S.C. Section 1320d et seq.), as amended.