I don’t know the percentage and I suspect no one knows it but I’m sure that a good percentage of American cat owners do not report it to their doctor when they are bitten by their cat and it has caused an infection.
They treat the wound themselves with anti-inflammatories and antibiotics provided they have the medicine or can get their hands on it without seeing a doctor. Bites can be serious because it’s a bit like injecting bacteria under your skin. Most often the bite heals up without complications because the body’s defences resolve the problem. Sometimes infection can take hold and you need antibiotics. For those you need to see a doctor normally. I don’t know the situation in America with respect to prescriptions for antibiotics. Perhaps you can get them online without a prescription. If so then I’m sure that a reasonable percentage of cat owners keep a packet of antibiotics to hand just in case.
At least theoretically, when you are bitten by your cat you should (a) see a physician immediately and take their recommendations and (b) check that your pet’s vaccination are up-to-date and (C) report the bite to the local health department and animal control authorities. Local regulations may require that your cat is confined and isolated for monitoring for signs of rabies.
It seems to me that the fear for cat owners is that their cat will be taken and confined to quarantine for, as I understand it, 10 days. It would also seem that a lot of cat owners don’t want this to happen and therefore take a chance because they’re convinced that the cat is not have rabies perhaps because he or she is an indoor cat.
In taking this action, and in self-medicating if the bite has caused a nasty infection, the cat owner is taking a risk on their own health. These infections can be nasty and a friend of mine says that they can turn to cellulitis which is a common, but potentially serious bacterial skin infection. If left untreated infection can spread to lymph nodes and bloodstream and can even become life-threatening.