Of course it covers your medical costs, that is the entire point of the requirement of the red license plate for taxis in the first place.
The required insurance covers all the paying passengers in the vehicle, otherwise they would not be allowed to be a legal taxi. That is why you should always take a legal, red plated taxi. Should a hotel or restaurant secure you a ride in a non-red plated vehicle, their business liability insurance coverage would cover you in case of an accident. But I would certainly ask that the establishment find me a red plated legal and proper taxi when asking for the ride.