I'm somewhat sympathetic to the idea of a given pharmacist not handing out the prescription, but only as long as the pharmacy has on staff those who will. And lying about another pharmacy is clearly WAY outside the bounds of appropriate.
I don't know what the law is in that state, but pharmacists making moral judgments before handing over prescriptions is IMO wrong on principle. How about they demand proof that a man getting ED drugs is married, and having sex with his wife? Denying birth control because they don't believe in it? Not filling STD drugs if contracted outside marriage? What if they don't believe in treating mental health with drugs, but want people turning to religion? Seems to me if you work in a pharmacy, you fill all legal prescriptions, THE END.
And the distance between her home pharmacy and the CVS and Walgreens is also a problem. When we discuss these things, we assume generally that some other pharmacy nearby will fill the order, so no harm no foul. But someone without a car might not be able to GET to one 25 minutes drive away, and why should they have to? The pharmacist isn't the doctor or the patient and unless their prescription is somehow unsafe because of interactions, fill the damn thing and do your job, not insert yourself into the doctor patient relationship.