Re: Sound bites bite back
If the airbag is deployed then it will be reasonable to expect the car will not be going anywhere under it's own steam again so if it is on the road the Police would be needed for traffic flow/recovery etc, if it's off the road then the accident is likely to be more critical.
Also any activation of the airbag should have an ambulance assessment for C-Spine injuries as the forces involved will definitely point to that mechanic of injury.
If you are sure you don't want the emergency services there then you can always call them yourself straight away and tell them there is no problem. It would be likely that the reason for this would be an intoxicated driver so the Police might just turn up anyway.