They can claim your dog is a nuisance and dangerous but a single event shouldn't support that. If you can pay the vet out of pocket you should do that. But draft up a letter stating that is the extent of it and get the other dog owner to sign it. That should help orevent any nonsense. Otherwise your insurance will go up and they may even drop you - your dog's breed could also come into play with the insurance company. Only bring them in if the damages were too much for you to absorb. As for the fence, you're correct in that the smaller dog on the outside COULD have stuck his head in but you've also admitted to a loose board and a dog that chases and barks along the fence. You'd probably lose that argument. Best thing is to affix some chicken wire to the fence to further prevent your dog's head or mouth from getting through. It's inexpensive and you can see right through it. Not sure if you're allowed, but hanging a Beware of Dog sign should keep people at a safe distance.