Whether I'd shoot a dog depends on the size of my dog and that of the dog attacking mine. If I'm walking Eve and she's attacked by a Pomeranian, I'm just going to kick the little dog aside. No need to hurt it if you can control the situation otherwise. If a big dog attacks Eve and is biting and making contact with her (not just approaching and making a lot of noise) you bet I'll use whatever I have on me to get that dog off of her. If I kill the dog in the process, tough cookies. I'm sorry, but MY dog's safety is my responsibility. Obviously I'd rather not hurt a dog, but I certainly could shoot one if it was hurting mine.
Letting them fight it out? Ridiculous. The only time I don't step in is if it's a seeming fear-aggressive small dog attacking my larger dog, because I know my dog will be able to quickly and easily put the dog in its place. I trust my dogs to be fair, but I don't trust a random dog-aggressive dog to be fair to MY dog if they were the instigator of the fight. I step in and end it as quickly as possible.
Yes I would report a bite like that. Absolutely.
I have nothing against DA dogs, but for the love of god, keep them on a leash and AWAY from other dogs.