All dogs are omnivores and predators, but saying they're all "killers at heart" is silly. Most dogs who run into a field with a horse cause trouble because they chase it and the horse is hurt trying to get away. Chasing another animal is fairly normal, typical dog behavior (and obviously one you don't want to allow), but attacking and mauling them is not.
A dog who grabs and mauls another animal as play not because he's hungry and hunting isn't just being a dog; he's being a POS who's a disgrace to the name dog. Not to let the owner off the hook, but the dogs aren't worth spit either.