What a rotten situation. If only you'd thought to be vague about which cat it was at the hospital... I'm sure they can't force you to name an animal.
Even now, I wonder if there might be some solution in you saying that it wasn't that cat, you were mistaken, or the hospital workers misunderstood what you said. If you said it wasn't this cat, but a stray cat you encountered somewhere, that might be the equivalent of withdrawing charges in cases involving humans. Even if the denial sounds like a lie to them, they have no way to prove you were bitten by this cat (you're the only witness), and probably no resources to try to prove otherwise.
In a pinch, though, having a lawyer friend make a phone call often solves minor situations like this without things having to go to a court case.
Even now, I wonder if there might be some solution in you saying that it wasn't that cat, you were mistaken, or the hospital workers misunderstood what you said. If you said it wasn't this cat, but a stray cat you encountered somewhere, that might be the equivalent of withdrawing charges in cases involving humans. Even if the denial sounds like a lie to them, they have no way to prove you were bitten by this cat (you're the only witness), and probably no resources to try to prove otherwise.
In a pinch, though, having a lawyer friend make a phone call often solves minor situations like this without things having to go to a court case.