I don't think it's true that they are back together. Especially after Kate and her mother were subjected to a constant barrage of negative stories seemingly 'issued' from William's circle and he didn't seem to do anything about it. IF they are back together, she is, for lack of better words, stupid. This would just justify my suspicion of her.
I think I read somewhere that William did issue a statement denying those allegtions coming from his friends, even calling Kate personally to apologize that these rumours are even out there.