Why can it not be Kati nincs hall?
Nem means "no" or "not". Nincs means something doesn't exist or there isn't any of it. Also, you can think of it as nincs= "nem van" (nem van is NOT said in Hungarian).
Wouldn't "Kati nem hall" be better translated as "Kati doesn't hear"? I answered "Kati nem tud hallni", but this wasn't accepted.
To me this sounds like you are saying "Kati doesn't know how to hear" which implies a different meaning. Hope this helps