A Fitness Trainer is not a good analogy either, because you can't stay in business long as a fitness trainer if you have no idea of the basics of fitness or anatomy. E.g. a fitness trainer who said that you breath through your feet, so you should wear sandals when running knows as much about biology as a nutritionist who thinks chlorophyll can oxygenate your blood. However the magic super food nutritionist had a prime time TV show! High ranking, popular nutritionists can believe things that are nonsense, what hope do you have about a local nutritionist?
And dietician's pushed the traditional food pyramid for years, which many current dietician's find fault with, years after nutritionist's pointed out the same thing.
I've met successful doctors, lawyers, trainers, etc., that believe in crazy wild theories that have no basis in anything other than what they want to believe. Success amazingly often has very little to do with if people are right or wrong (I'm sure there are some very wealthy astrologers out there).
By your theory, it doesn't matter which doctor you pick, they are all trained physicians, so they all believe the exact same thing. Need a psychologist, just read Dr. Phil's book, he's board certified. Or don't agree with Dr. Phil, then all psychologist's are bad.
I get what you are saying, but formal education only tends to weed out the absolute nutjobs.
Just look at Dr. Oz or Charles Poliquin. Completely crazy.
TLDR: Ask for proof. From my experience you overestimate the impact of formal education.