Notso, imho you are quite correct.
The first ambulance manager at the scene was clearly not trained to make the right decision, though I don't doubt his professionalism and good intent. Perhaps a tower controller or other aviation professional, maybe even a dedicated individual with emergency response training would be better suited to the task.
However, the manner in which you are voicing your views is one that is bound to produce the inappropriate vitriolic responses found here! I just hope you use more diplomacy on the flightdeck...