It probably depends on what kind of therapy is being performed. If there is any surgery involved, even minor surgery, things can go wrong. Infections could build up, allergic reactions may occur, etc.... Those performing the therapy, probably, know they could be sued and put out of business without having parental/ adult consent. Verbal agreements mean nothing. If there is not a signed consent form then, basically, the agreement never happened. It is a protective measure for minors, as well. They may not truly know all of the dangers involved in having beauty therapy.
