If you don't think so, it's only because you're not thinking, you're reacting. To people like that, your chickens are YOUR problem, it's only when they have to deal with something that it becomes THEIR problem, and yeah, their dog looking like a circus clown and rubbing that dye all over their house is, in fact, THEIR problem.
The dog getting hurt, grounds to press charges - you won't be keeping chickens after an animal cruelty charge, so that's one way to solve the problem, I guess. The dog killed, not an ongoing problem, just an excuse to go nuclear.
And you've clearly never used a motion activated sprinkler. It has a short little feeder hose. Put some gel food coloring in there and hook it back up, thirty seconds.
And don't act like dogs are the only thing out there. If dogs can kill your chickens., so can everything else on earth. Animal owners need to keep their animals safe, and that means fence, regardless of the predator. Land owners who keep livestock, need fence.