How long would have taken for an RAF Sea King to arrive at the scene of the aircraft as compared to the time the Jig Saw aircraft arrived?
If you go bobbin in the oggin you will have to wait a bit for help to arrive no matter who it is that turns up first.
Now grant you....the transient time for a rescue boat to make its way 500-1000 meters away from a rig should not be all that long one would think....assuming the boat was on the rig to begin with.
Where were the assets located when this thing kicked off that night?