Can a non-physician own a med spa in Utah?

Short answer
The cited rules do not settle this — they bar an owner with a financial interest from substantially interfering with a physician's practice, and in a professional corporation limit shares and officer/director seats to persons the licensing act allows.

Utah reaches the outside owner through interference. Section 58-67-501 puts within “unlawful conduct” the act of substantially interfering with a licensee’s lawful and competent practice of medicine by any person or entity that manages, owns, operates, or conducts a business having a direct or indirect financial interest in that practice. It reaches contracts too: entering a contract that limits a licensee’s ability to advise patients fully about treatment options is itself unlawful conduct. And the fee rule carves out the legitimate structures by name — nothing in it precludes the legal relationships within lawful professional partnerships, corporations or associations. And the professional corporation act restricts ownership directly, not only through interference. a person may not be an officer, director or shareholder of a professional corporation unless licensed to render the same specific professional services — medicine and osteopathic medicine count as the same service, so an M.D. and a D.O. may hold shares in one entity — and the single exception is that a nonlicensed person may serve as secretary or treasurer. Shares may be issued or voluntarily transferred only to those licensed persons, or to others to the extent the applicable licensing act allows, and “Any shares issued in violation of this section are void.” The corporation may render professional services only through licensed officers, employees and agents. These claims survey Title 58 chapter 67, one division rule and §§ 16-11-7 to 16-11-9; they do not survey the rest of Utah’s entity law.