I don't think that is completely true. The Rat terrier I mentioned above would chase the big Montana Jack rabbits as long as he could see them, every time. If the rabbit jumped down a coulee or made a turn over the hilltop or behind the weed patch the dog would loose him. Definitely a sight trailer. He only caught those Jacks if he surprised them. That was interesting in its self since my Rat Terriers and the Montana Jack Rabbit are about the same size. He lost more than he caught.

My friend took a video of this dog jumping a Jack rabbit and chasing it to the end. The Jack took off across a wheat stubble field in a big basin. The Rabbit ran a large circle around the basin and head back to where it was jumped. The dog never lost sight of the rabbit. The chase was 4 or 5 minutes long. The rabbit intially pulled away from the dog. In the middle of the chase the dog and rabbit maintained separation, in the last part of the chase the dog can be seen closing ground. Finally the rabbit got back to the starting area and just stopped. The dog was right behind and nailed the rabbit. After the rabbit was good and dead, the dog laid down beside the rabbit and rested for about 10 minutes and went back hunting.

I do not think you could break these dogs of chasing and killing once they were allowed to do it or especially if they were trained to it. For this breed it seems to come naturally. That was part of the reason for the keeping them fenced in. If I had let them run they would have not stopped at anyones property line as long as they could find a small animal to kill. They would have become that "Feral dog" that wonders in and gets shot.

They have never been allowed to roam free becasue I'm sure they would not hesitate going to the neighbors and killing their cat or least chasing it.