I have a genetic disease that shows up in 4/100k people, so rare, but not that rare. Any sizable town has at least a few dozen people with my disease.
In my experience, "an order of magnitude better" in specialists means they've at least heard of it, but know nothing about it. Every time I move, I have to spend some time educating my new specialist on the disease. I know damn well that every time one of them excuses themselves in the middle of the exam, they're going to look it up on the internet. It's pretty disheartening.