Did you miss the "landowner agreement" part?
They must not like their dogs very much. I couldn't imagine having coffee with my neighbors and saying: "Hey, if you see my dog running around away from my farm, I would like you to kill it and if I see yours out and about I will kill it too." "Now who would like a doughnut?"
A week later:
Rancher #1: "Yeah I saw your dog Toby out running around a ways away from your farm so I crushed him in the skull with my 30-06." "There was red mist everywhere." "You are welcome."
Rancher #2: "Oh thank you so much for killing him." "He was my son's favorite dog and I liked him too, but an agreement is an agreement." "I can't wait to get a chance to test out my new .270 WSSM on your dog when he gets a little ways from your house."
"I am glad we can do each other such favors!"