We still don't "know" that penny wasn't harassing livestock. We have the newspaper articles saying she was, and you saying she wasn't.
If she was harassing livestock, and had done so in the past, legally he did have the right to shoot the dog.
As to the some people/most people issue, popular opinion does not make something legal or correct. If everything hinged on the opinion of "most people" we'd be left with mob rule.