I disagree that a good doctor needs to be skeptical of everything until they properly gathered evidence. That is more a description of what a rigorous scientist should do.
There is a school of thought in medicine among some doctors (at least in Central and Northern Europe) that many patients know what’s wrong with them and one can go a long way toward a diagnosis by listening to and trusting a patient. Tests are used to confirm the diagnosis if possible, but they are well-known to be less reliable than the patients’ own experience (pains and other symptoms, for example). As an ex-medic myself, I strongly believe this is a more correct way to practice medicine, at least until significant advances are made in testing.
That is not to say that we don’t have highly accurate tests that will clearly indicate conditions (blood tests for IgGs, IgMs, BG, CRP, organ function, BP, ECGs, etc). But many conditions won’t show up reliably in common examinations and tests.
One of my old and wise doctor colleagues from a long time ago used to say that we live in the Stone Age of medicine — most of our tests and exams have very low specificity and we must treat a lot of people by what they tell us and our own subjective experience. He used to say that future doctors will see us as benevolent cave men who were constantly failed by our tools, unable to effectively remove illness and suffering, only really able to effectively listen and try to help, sometimes by just trying therapies until something hopefully sticks. I agree with them.
There is nothing worse than a distrusting doctor who dismisses the patients symptoms to instead blindly and arrogantly applies a schematic based on assumptions that our testing and examinations have very good specificity. That is just not the case for most diseases and violates the benevolence principle considered intrinsic in medicine by many. In my opinion, this is only acceptable for new doctors (like those still in training and under supervision). Otherwise, this behaviour is just malicious.
The science of medicine is very different from practicing medicine. The consequences of malpractice are deadly, and the time to treat a patient correctly is often limited. Scientists work in a much less constrained environment. Applying rigorous scientific method has relatively few negative externalities.