I click "Find Replacement" of the Doc, then I click the Staff Type "Youth Trainer".
Then, I find that the display of Specialty is the same as Doc.
https://imgur.com/SXsTVKm If I click "Hire" of the Secondary Staff and click the Staff Type "Doctor", then the Specialty only displays two options.
https://imgur.com/yS9DyIuIt seems that it is a bug.