Absolutely agree.
I will refill (most) meds when reasonable, and when the request for a refill comes from the pharmacy.
If I have to re-write (e.g. for "mail-in" pharmacy) or change the prescription, then it is a new prescription, not a refill and the patient has to make a visit.
I almost never respond to patient requests to "call my pharmacy and refill my meds" type calls -- not even if they say "please".