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".
Mmm well, it's not wrong, but it's hardly ever used.:/ I wouldn't suggest you using that form of γιατρός. Unlike ιατρείο or ιατρική, ιατρός is very hard for someone to come across.
It's only doctors themselves who use it! :-D They must imagine it adds prestige LOL!
But Greeks do feel proud when they see words like "iatrogenic" etc in foreign texts, so it'd be a shame if we ever let such words of our own language die out ;)