Most supervisors don't do the level of patient care that the ambulance providers do. especially administrative supervisors. the reality is, even if your supervisor is a paramedic, if he or she doesn't get on an ambulance regularly, and regularly see and treat patients, you will probably know your protocols better, be more up to date on latest techniques, and be a better provider than the supervisor, as well as be more in tune with what the best treatment plan is to treat the patient.
EMT supervisors are acceptable as operational supervisors. Akulahawk said it perfectly, "I'm OK with an EMT Supervisor telling me to do my job, however they will not tell me how to do my job." Clinical QA is best reviewed after the call, regardless of if the supervisor is an EMT or paramedic. At the patient side is not the place to argue over what should be done to treat the patient.
If the situation you describe, I would have done what I thought was best, and then had a sit down with administration the next day to discuss what happened. if it still didn't go the way I wanted, than I agree, resigning is the best option.