False. I've lived with three Saints. The first one, back when I was a small child, on a few occasions herded sheep into a swamp and killed and ate one of them. One time my aunt had to beat him over the head with the flat side of a shovel to get him to release a neighbor's retriever who's head he had locked his jaws on to. He would also swim out into a near by lake for carp. Although I never saw it, people fishing there told us he looked just like a grizzly on a salmon run. He was always my loyal protector. I still have picture my mother took of me riding him like a pony.
The last one, who died this spring at age thirteen of hip displacia, took a neighbor's loose holstein calf. She was so patient and loving my infant children could and did crawl up to her, take the bone she was chewing away from her, beat her over the head with it, and then crawl away with it! All dogs, like all people, are capable of killing. These particular dogs are the most loyal I know and they can clearly separate people from game. I've never met a bad one.
A dog who has attacked stock is dangerous, even if he doesn't attack his master. My dad and I lost a whole flock of sheep one year because of dogs like this. In Indiana, if you catch a dog killing stock you are allowed to shoot them. Harsh, but based on years of country experience with dogs like this.