At the time Sisko was on a leave of absence, and therefore wasn't considered "active duty." Any first response to a call to the New Orleans Emergency Services about a human male stabbed outside Sisko's Restaurant should have been from the civilian police and EMTs, not Starfleet.
That's assuming that the equivleant of today's emergency number was called. Isn't it possible Starfleet Medical was directly called? What are they going to do if that was the case. "Please disconnect this call and contact your local emergency services?"