Hair, I am NOT exagerating. Such things happen, sadly, quite often. The police CANNOT safely assume that such events ARE innocent... for their own safety and that of the public, they have to assume worse than innocent. The police responded as if it MIGHT have been a carjacking because carjackings DO HAPPEN and people DO GET KILLED. An attacking or advancing dog may be innocent (actually all dogs are innocent) but it is still a very real threat and potentially extremely dangerous.
I assure you that the dogs that I have owned would react extremely aggressively and angrily if one of their people were being treated as the police were treating this family. The police cannot yell "Halt, or I will fire" to a dog... he cannot understand and will continue his agressive behavior until someone with authority HE recognizes stops him.
Someone posted that he, personally, would allow the dog to bite him first, before taking action. That's nice, but the police do not have that luxury... nor should they be expected to take a potential arm-breaking bite before acting. Police officers are permitted BY POLICY to use deadly force to prevent injury to themselves or others... they do not have to wait for the injury first.