There are lots of people that are capable of shooting from a moving helicopter and hitting the target. They worked well in Viet Nam, and there are a good many capable of shooting from either a prop driven airplane or a helicopter and killing game or shooting darts to immobilize critters. I would have no reason to believe that the LEO assigned to police helicopters were not among them
For me, that is the one element of the story that doesn't make much sense. If you are trying to stop a fleeing pickup, why would you shoot at the bed?