Wow. As a renter for many years, I believe that if I do not find the condition of a unit acceptable, I'll make sure the management knows the same and demand changes. I and my wife spend about an hour every 3 weeks to steam-clean the carpets in the apartment we are renting right now because we have a dog. I wonder how 6 hours of deep cleaning would be enough after a Year's lease. By the way, hypoallergic breeds of dogs do exist to. There's a difference between having a Greyhound and a Lhasa Apso. Its about what remains after the hair is cleaned (dander). I do not know what tone she took with you, but the least you can do is go over to the apartment yourself (females do have a better sense of smell in most cases) before you decide whether the carpet is good or bad.
I also find it appalling that everyone here declares the renter will be a problem renter. Why? It's within the renter's right to demand something even if you are not legally bound to agree to the demands. Its up to you to tell them that you don't agree with their claim, that you feel the needful has already been done, and give the renter an option to continue or leave. That, I feel is the right way to handle it. The renter is the paying customer and just like in any other business, its your duty as a service professional to be able to handle their not-so-friendly behavior. If the person recorded the phone call, and she was the one taking a threatening tone, its not going to help her much anyways.