I would think that ethically they would be required to say something like "That's not really my specialty but I can refer you to X who has a lot of experience" or something along those lines.

I know it can be unethical to treat certain patients if you can't get over your bias and you feel it would be unfair and possibly detrimental to their recovery to work with you. My T does not work with children because of her past, it's too painful for her, too triggering, so she refers out to people she knows who are skilled with kids. They reciprocate by referring adults to her.