I'm arguing that a sufficiently comprehensive system would take in to account whatever that doctor realized (and perhaps much more) and compensate for it when determining expected outcomes.
A simple illustration: I have medical issues with no meaningful diagnosis, despite seeing many doctors. If the medical community can't figure out what's wrong, how can they have an understanding of all the relevant factors in determining risk?
This isn't directly related to your point, but why is this even the norm? Why are you going from human to human seeking answers to some arcane mystery like you're on a Skyrim quest.
Imagine a system where you wouldn't need to see any doctors. You would type in all of your symptoms as accurately as you can with as much detail as you can, perhaps with a timeline, and as output you'd get the most likely causes (a diagnosis). Maybe that system would even have your medical history (and that of other people and related diagnoses) to better predictions.
It seems to me that a system like this would be significantly better than going to a couple of humans that are arbitrarily local to you and asking them to figure it out. It is slowly improving all the time just in the form of Google and WebMD. Even before 2010 I accurately diagnosed myself with Bell's palsy with the internet and the doctor begrudgingly asked how I had made that diagnosis. Confirmation from the human doctor was nice but redundant.
I'm also arguing that it's not just a psychological resistance to a data-based evaluation system. That people understand the system would be subject to being gamed, and the overall quality of the work would actually suffer. (A bit analogous to how peer-review and the tenure game has interfered with good science practices.)