Was Officer Cox really a local cop?
It occurred to me: I don't think Officer Cox was really a police officer, at least not one that lived in Cradle Bay all his life.
He didn't seem to know Dorian Newberry beyond his the Janitor/rat catcher role. In the deleted scenes, Newberry was actually the school's old counselor. If Cox was a local, he would have known who Newberry really was and seen through his stupid act, or at the very least had kept him in his sights when he tried to take Steve and Rae at the gas station.
Plus, when the guy reported the deaths in the beginning of the movie, he used terms that no cop uses (that I've heard of). Cox seemed more like a prison guard, hospital orderly or CIA Agent than a cop. It wouldn't be a stretch if he really was a cop who was dirty and chosen for his moral flexibility.
Caldicott replaced Newberry at the high school, and those people at the hospital didn't seem to be locals either. It's possible Cox took the place of Cradle Bay's police chief when he "retired" or had a heart attack or was killed in the line of duty.