A couple of points.
I tend to view the treatment of dogs and children as two of the best indicators of a persons worth. Those who feel the need to be needlessly cruel to either are not worth much. It is ok to shoot a dog under pretty much the same circumstance in which it is ok to shoot a man. If they are putting you and yours, or even you property, in danger then it is acceptable to shoot. One should try less extreme methods if possible though. Dogs running deer or even cattle can be delt with far more decently than just shooting them. Domestic dogs are, as a general rule, pretty good about stopping what they are doing when a human yells and approaches. Those to dense for that are often gun shy and can be ran away with a shot into the ground. People shooting dogs to stop them in these circumsances without trying to run them off are just being mean and lazy and would probably like to deal with annoying people in a similar manner.
As to the hunters shooting dogs. I would have no trouble believing this out of MANY deer hunters. Before anyone gets up in arms over that statement I to hunt and that includes deer. The ones I'm refering to rarely hunt anything else and tend to view deer hunting as some sort of religion. We have a lot of them in the part of ky I live in. Many of this same croud get bore and shoot at whatever is near which can include vehicles, cattle, and pets, as well as carelessly discharging their weapons in the directions of other hunters. These same people are the ones who litter local road sides with deer carcasses and make the rest of us look bad to non hunters. I know quite a few hunters who avoid going out the first week of modern gun deer season due the very high concentration of these types then. I also know a guy who likes to hunt squirils with a dog but has to wait until archery season is over on account of bow hunters trying to stick arrows in his dog which is scenting squirels and NOT chasing those beloved deer.
Some dogs actually do stay on their home property. Our neighbors dogs are not fenced or tied and they don't leave their land. Our dogs do leave our land but the territory they range into belongs to a friend of ours who is fine with them. Actually our free range dogs do alot to keep agressive strays, coyotes, and crop eating from getting to comfy in the valley, all while leaving alone other pets and livestock.
Best of luck with the jerks who messed with your dog and I hope he turns up.