What kinds of non-moral reasons should they use, then? Or should people be able to legally buy and use all legal medicine freely?
"Non-moral reasons" is shorthand for reasons that do not involve morality that is not intrinsic to performing the duties he is being paid for. For instance, "I refuse to give the patient drug X, because drug Y will cure the patient and drug X will not" is a moral reason insofar as wanting the patient to be cured is a question of morality, but it would be okay. "I refuse to give the patient drug X because God tells me not to give people drug X" would be an unacceptable reason. This actually happens for contraceptives.
One sol...
Over at Scott Adams' Blog you can find a very fine example of using the 'Rationality Engine' to solve the social problem of assisted dying.