I think that the primary correct translation here should be the secondary correct translation.
This sentence means "My friend has become a physician". The secondary correct meaning is, "My friend has become a doctor".
I myself am a doctor of philosophy. I am a doctor. I am not a γιατρός. Only a doctor of medicine is a γιατρός.
The primary translation reflects authentic English usage. If you say "she is a doctor", it means she is a medical doctor. Holders of a PhD get the title "Dr" before their names, but that doesn't mean the noun "doctor" is used of them.
This is true even in academic circles - you'd say "he has a PhD" or "he has a doctorate", not "he is a doctor".