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Yes we do. They aren't hiring OP and they aren't representing the school. They are a personal entity being asked to perform a mentorship type task. It's a completely voluntary thing, and they don't have to write it regardless of their reasoning.
And this is all assuming anyone can definitively prove, without a doubt, that the SOLE reason they won't write the letter is discrimination.
My school has a policy for reasonable accommodation for those with disabilities. If the doctor cited the reason for not writing the letter because the student couldn't lift a patient, there would definitely be an issue there.
Again what I mean to say is, we don't know the details here.