Did you examine the video tape? There were at least three armed LEOS on scene, one with a shotgun trained on the family members/vehicle. The *family member suspects* were basically already neutralized, on their knees and being cuffed. A small dog exits the vehicle and this LEO blows it's head off, the shotgun blast caused the other LEOs to all jump, as if they were under attack.
Let me tell you something pal, these family members came very close to being all shot to death. Don't you realize that a gun shot being fired at a critical time could cause all or some of the LEOS on the scene to unload on the suspects? Happens all the time.
The LEO that killed the dog is an idiot, and almost caused his partners to kill off this family.
All for what? Being afraid of a minor bite from a small dog?
Have you ever seen what kind of minor bite a small dog such as a forty-pound pitbull can inflict?