Being an aeromedical operation, you wouldn't want to refuse to do an evacuation and have someone croak. THAT would get you sued for sure.
A better strategy would be to fly the patient to somewhere nice for his necessary treatment, plead fatigue and check in to a 5 star pub with the aeroplane parked until the boss got the message and paid up.
The worst could happen is you get fired, but if you are not being paid, what the hell anyway?