How can I fight a landlord claiming we had an unregistered pet?

My roommate and I moved out of our old apartment on Saturday. While we had an appointment for a walk-through, when it came time, our property manager was "too busy" and she would do a walk-through later that day, Initially, her istant called us to say that everything was fine. However, she called back today to tell us that there were numerous cat urine stains and a strong smell of cat urine throughout the apartment, and since we hadn't registered or paid for a pet, they'd be fining us for that as well as for carpet cleaning. Here's the kicker - my roommate's allergies are so severe that it is physically impossible to have a pet of any kind - even being around someone with cat hair on their clothes is enough to send her into a severe allergic reaction. We have two allergists who have treated her and will attest to this, but we're not sure it'll be enough. I'm positive that we didn't leave any stains or odors behind - we cleaned the apartment top to bottom before leaving. Does anyone know how we can fight this obnoxious he-said-she-said situation? We didn't have so much as a pet rock, but one can't really prove the absence of something.