We have this sort of problem in our neighborhood, too - where people let their dogs off leash, and don't take complete responsibility for them. While walking our dogs (on leash) we have had numerous dogs, off leash (sometimes supervised, sometimes not) run across streets, yards, fields, etc. to 'visit' with our dogs. It's usually a friendly visit, but not always. The worst time was when an off-leash GSD ran across a street and got right in Paula's face. She was so startled that she backed up and slipped out of her collar. Luckily, she came back to us, but if she hadn't, if we had lost her or if she had gotten hit by a car and injured or worse, I would have sued that dog's owner for every penny I could get. Not that money could bring back my dog, but simply because owners like that need to take some responsibility.
In your case, you had to pay $200 because another dog attacked your dog ON YOUR PROPERTY. You are completely justified in suing that owner for expenses.
My husband and I have talked about this type of thing, since we do have so many incidents with off-leash dogs, and we have concluded that, if there was ever a fight that broke out because an off-leash dog approached our leashed dogs, we would definately go to the owners to pay the veterinary expenses!