You are not providing licensed medical services. Just come out and say it, since it's true. Yes, saying that will cause people to distrust you, and well it should. You are right about there being a shortage, but there is no substitute for a real doctor.
That said, being upfront about it instead of trying to beat around the bush or make excuses doesn't help you. It only serves to make you even more untrustworthy. Your attempts to obscure the fact that you aren't providing real medical service only suggests that you know in your heart that what you are providing is not the same. If you believed your "coaches" were good enough, you wouldn't have to do anything at all to hide the fact that they were not real doctors. You could just come out and say it.