I am not a doctor, by any stretch of the imagination. But I do work on cars, and computers. As far as I can tell, a doctor works exactly the same way as a mechanic or a computer technician. They listen to symptoms, make an educated guess at a root cause based on limited information, make an educated guess at what might resolve the situation, and then wait to hear back if that fixed it; if it didn't, the loop continues.
Medicine might be scientific, but the practice of medicine is clearly an art, not a science. I don't trust my mechanic; why the hell would I trust my doctor?