Two definitions of intelligence I like are "being able to choose actions that steer the future toward outcomes ranked higher in your preferences" or "being able to squeeze the future into a narrow range of possibilities."
Or, alternatively:
(1) the ability to precisely realize one of the members of a small set of possible future worlds that have a higher preference over the vast set of all other possible worlds with lower preference; while
(2) using fewer resources than the other alternatives paths for getting there; and in the
(3) most diverse domains as possible.
Accordingly, when we discuss the intelligence of medical professionals, we run into two different possible problems from the perspective of the patient.
One: the doctor may simply not be very intelligent. Yes, it's true, doctors have quite a bit higher IQ on average than a plumber, but IQ only measures one aspect of intelligence -- a high IQ is required to be intelligent, but a high IQ is not a guarantee of intelligence.
Two: you're just another patient in a long queue of patients. How highly does your doctor really rank your good health in his preferences? How much of his limited mental energy is he likely to spend to make sure the future is threaded through the eye of a needle that it needs to pass through to make sure the outcome is your continued well-being? Depending on your condition, it could be a massive needle with a huge eye that almost no effort is required to go through, or it could be a tiny needle with an even tinier eye, where the doctor will truly have to be exceptional for you to survive (or for your condition to be cured). A person can be as intelligent as anyone, but if they aren't willing to use the full powers of their intellect for your sake, that does you little good.
So, then; we have (1) ability and we have (2) investment or interest. For the difficult cases (contained within this definition are cases that aren't difficult to treat per se but are often mistaken for something else) you need your doctor to have both 1 and 2. Note that this applies, to a lesser extent, to even something like the common flu. Sure, you might not die if your physician doesn't give it his best, but you could get better sooner. Hence why it's important to not hero-worship, to not just transfer final responsibility to someone else, but to treat the doctor as you would another craftsman, like Kalam says: let them do their work, but be the final judge. You wouldn't take back your car if it was broken even if a mechanic told you it's working perfectly fine now. Likewise, if you're told your car needs an expensive part X, you'd be wise to get a second opinion or do your own research before trusting one mechanic blindly.