I live in the sticks, a rural county, and yeah, some folks call the po-po about just about everything.  If you are small enough you may not have an dog warden, or game warden to take care of some of the incidents.  

If the neighbor's injured pigs were routinely getting out and displaying their injuries to you, then once ok, numerous times, yeah that's cruelty.  And animal cruelty should be reported and dealt with.  Maybe the people just need to be told that if their animals are subjected to more attacks by the dogs, the dogs may be deemed dangerous and then they would need to do certain things to keep them from attacking people or animals.  

SSS is Shoot, Shovel, Shut up.  This is what the game warden said to my dad if he runs across any dogs running deer.  Shoot the dog, bury it, and say no more about it.  It's awful because people do want to know if their lost dog is starving or injured in a ditch somewhere, caught in a trap.  But on the other hand, dogs are very bad if they start running deer.  They can run a deer to death, and there is a reason that hunters are encouraged to shoot the dogs if they are running deer.  

That would never happen here. It’s like hearing something completely foreign to this state.

I’m meaning the callers shouldn’t be going over to their neighbors property and shoot their neighbor’s dog... and the pigs don’t deserve to get shot for escaping an animal attacking them 

Clearly it’s not a good thing but SSS is more for if the dog came over and attacked their livestock. And even then unless it’s going to cause a bigger issue I wouldn’t go with SSS. I might still shoot the dog if needed but I’d not hide the fact because I’d make the owners pay for the damages