...With Psychology/psychiatry being a branch of medicine and all.
Psychiatrits are doctors just like cardiologists, neurologists etc.
Psychology is not medicine.
She may fall under Beverley's staff, once she started wearing a uniform it was the medical colors.
She wasn't wearing medical colors, she wore science blue. Crusher was in charge of the medical staff (except for the nurses, wouldn't make much sense to have a doctor be their boss), not everyone in a blue uniform.