To the OP, fabulous post! I am sorry that your child had to go through being bitten - it is a very sad experience for everyone involved.
From an owner standpoint, I felt like I should point out that vaccinations come into play anytime that a dog bitch is involved. None of my dogs have ever bitten anyone (thankfully) but any dog will bite under the "right" circumstance. Whenever you are bitten by a dog that does not have vaccinations, or is not confirmed to have vaccinations (aka papers from vet in hand) I would INSIST on rabies treatment. If your dog bites someone (and this includes all owners who rely on holistic methods and do not use shots) your dog could very well end up dead for testing purposes.
I also should mention that I do not trust off-leash dogs EVER not to bite- especially when the owner is nowhere to be seen.
"Dogs have given us their absolute all. We are the center of ther universe. We are the focus of their love and faith and trust. They serve us in return for scraps. It is without a doubt the best deal man has ever made." - Caras