4/100k is still exceedingly rare. There are probably 100s or more diseases that show up in 5/100k so it's hard to know them all. Meanwhile the doctor probably sees the top 15 diseases all the time..
My girlfriend has a condition that affects 12% of the female population to a varying degree. Some doctors knew absolutely nothing about it. Some were able to solve it easily.
To be fair to (most) doctors, especially your primary physician, have to diagonose a huge range of conditions. The edge cases are rare and so they are not as well versed on them.
System specialists are an order of magnitude better. I.e. going to an Ear, Nose & Throat doctor if you have Asthma.
Disease specialists are the pinacle. Sometimes these are researchers rather than normal doctors.