The rescue by family was apparently over by the time the "SWAT team" arrived. Wouldn't be the first time a dead guy has held a SWAT team at bay for a while. Remember Andrew Cunanan? They took their time storming the houseboat in which he had holed up and killed himself.
You are right. Some police who were also searching in the area arrived shortly after the victim was rescued. A description of the events is included in an article by the photographer who happened to be there. The surprise refers to her surprise when they rescue happened unexpectedly right in front of her. She and her colleague ran away from the gunfire, but did get pictures a short time later.
Leslie Westbrook: Photographing Bethany Arceneaux rescue a surprising, emotional experience