cooperplace.
I think you sum up the situation well.
My daughter is also a doctor and on flights with various carriers has responded to several calls for a "Medical" doctor.
She does not carry medical ID but always offers her UK doctors registration number to allow the crew to contact the ground if they decide to check her credentials
She too is used to being in command and I feel sure would soon resolve any situations that might occur with crew.
I have seen her in action at a medical emergenvy in the street and was more than impressed.