That may be true but there was an artical(Forgot where I read this)where a guy broke into someone's house, and the guy who owned the house sent his pitbull after the burgler, the dog killed the burgler and the home owner was charged with man slaughter w/intent.
Things differ on a case to case basis. Adding domesticated animals, which are considered weapons in a legal sense, complicates matters. If you are in a state with a form of the Castle Doctrine or a "Make My Day" law, simply shooting or killing an intruder by your own controlled actions will be justifiable.
Things can get complicated with these laws:
Chasing them down and killing them or defending a neighbor's property are both grey areas that have no legal definite. In this particular instance, he was acquitted.