I do think that Cupid should have offered to pay any medical bills on the spot - it sounds like there wasn't much communication between Cupid and the other dog's owner, and therefore I am not surprised they want to file a police report because I would have absolutely done the same thing if the owner didn't offer at least that. And I will say, Cupid, that you are coming across like a child who doesn't want to get in trouble. I can understand that you don't want a police report on your dog, but you clearly understand that this was a bigger deal than you want it to be. Stating that it wasn't after creating a whole thread doesn't mean that it wasn't, it just comes across like denial. And now you've called them more than once - what if they have caller ID, and after they figure out who you are, go back to call that person who called several times about the incident and realize it was you all along? How do you think you'll come across then? It's been less than 24 hours. There's still a good chance that medical issues will come out of this, which might be why they want to file a police report because they'll want a record of this if they want to go after you for the costs. If I were you, I would call, confess, and then get the phone number of the people whose dog your dog attacked and call to apologize and tell them you want to pay any bills that come out of it. Leaving it alone and hoping that they're too disorganized to figure out how you are and come after you is really childish and, in my opinion, greatly increases the odds that your dog will end up with a police record.
I am also completely against just returning an animal that is tough to take care of, especially if the animal hasn't actually harmed anyone yet (addressing other posters, not you, Cupid). Pit bulls are known to be aggressive. A person who knows this and chooses to adopt one anyway has full responsibility for it. You took on that responsibility when you decided to adopt a living thing which needs a home. If that dog then turns out to be aggressive, you cannot just return it like a vacuum cleaner. It's a living being, and it loves you. How awful.