Besides the other responses so far, consider this: the consequences of mistakes about this are asymmetrical. A doctor could be exactly correct about the probability of "making it up", but the cost to the patient of a missed diagnosis is not balanced by the benefit of correctly dismissing other cases. A conscientious doctor could try to consciously account for this, but there's no feedback making them get it right (and pressures against, in our current reality).

Also, when a patient succeeds in getting a correct diagnosis after trying multiple doctors, the previous doctors generally will not find out about their mistake, so there's a bias against them actually learning the right probabilities: you can expect them to be overconfident on this score.