“Lots of ways to help people. Sometimes heal patients; sometimes execute dangerous people. Either way helps.”
-Dr. Mordin Solus, Mass Effect 2
The Doctor didn't do anything wrong, even if they had the disadvantage for Hippocratic Oath, since as it is written it says: May not harm any patients under my care, must treat all patients equally to best of my ability, never use poison or false medical treatment to harm anyone. This is from the core rulebook, the doctor shooting the terrorists doesn't break those limitations.
This does sound like the Narrator threw a hissy-fit at being outthought.
I've had players (not just playing medics) pull similar stunts on me. So what.
If anything, the basic premise of the situation seemed to be weighted as 'no win for you, haha haha, the terrorists shoot hostages on YOUR watch'.
When the game turns into Narrator vs. Players, it's probably time to walk.
And in case you're wondering - I side with the doctor on this one.