Machine logic for health might be a very dangerous thing.. Humans have a thing called nuance .. I don't expect devices to develop this soon.
But humans are also prone for errors, e.g. just overlooking an important result from a blood test. I also think doctors won't be completely redundant for diagnosises, but I am convinced that in future, they will only be needed to confirm a diagnosis.
It really depends on how the analysis is done as well. When you take a blood sample or something and that is analysed, machines can just display the facts about that blood and draw conclusions. When a user has to explain/input symptoms, then it gets more difficult like you said. So i think it should be a combination, first/basic analysis by machines and AI, if there is no certainty a person can come in to do more diagnosis.