I myself am very fond of dogs, have one and probably lways will, but I know that they can infact damage property and livestock and for those of us who hunt can ruin the properties ability to contain game... Although I am not sure of the particular circumstances, Shooting Rabid dogs is not uncommon and there is nothing wrong with it. They can pose safety risks to some, liability risks, risk of property damage... The Farmer not being the owner of the dog could not have possibly been able to tell its reactions to situations and whether or not it would damage his property, or pose a risk to himself. I have been in a similar situation several times before and if I see a dog harassing livestock/Game on my property without visible ID (Tags) I believe there is nothing in anyway wrong with shooting it. If within his rights which by the sounds of it it seems to be great, if on the other hand it wasn't he should be punished by law...
That though is my opinion