FDNY EMS, and NYC Health and Hospitals Corporation EMS before the merger, had several incidents of NYPD canceling EMS responses, even when EMS was on the scene, but had not made patient contact.
Policy was enacted, that, if the patient had not left the scene by "other means" (feet, car, bus, subway, whatever), EMS had to, at minimum, hear the denial of request from the patient in person. Better yet, do a patient evaluation with running explanation that they could still sign the "Refused Medical Assistance" (RMA) on the call report.
If the crew did find something of concern, of course, they would make all attempts to convince the patient to go to the ED with them, or at least have someone take them to the ED, or their own doctor within the next 24 hours.
The usual mantra of "document, Document, DOCUMENT" would, of course, be fully in effect, but even so, if the RMA was signed, even with the knowledge of the OLMC MD agreeing with allowing that patient to RMA, EMS has been sued by the patient or their survivors.
I note Mobey specified the scenario as an MVA. In an instance like that, FDNY, FDNY EMS, and the NYPD, will all do their respective "thang" in dealing with each ones' specific areas of responsibility.
FDNY won't allow themselves to be canceled by another agency, once on the way, they will "continue in" to check things out for themselves.
EMS can advise the NYPD, on certain calls, that they won't be needed for that call, and return them (NYPD) "back" to 9-1-1 system availability.