My take on the mother: That it was the mother pushing the sexually oriented questioning (transcript - the radio show presenters actually didn't really encourage that line of questioning specifically, though the didn't exactly discourage it either...) gives some indicator that the mother might have been doing it as an attempt at punishing the girl for being a difficult kid (funny that, growing up with the kind of mother who'd force their kids onto lie detector on radio etc).
I also don't think it was a hoax, since I've met plenty of parents who would happily subject their kids to this sort of shit. There are fuckloads of terrible, terrible parents out there.
Muz: It was really less a matter of poor luck than it was completely retarded decision making. To be completely honest, the revelation that she had been raped was probably the sole good thing to come of the whole incident (even though it fell apart later). If she hadn't cried rape, the show probably would have gone unnoticed by the general public, the staff would continue exploiting and screwing with people on their show and the girl would probably still be unremarkable in the eyes of child protection services (No charges but you can bet your ass someone's keeping an eye on them now). My personal gripe was that the girl was forced into a position by the radio program where she had to discuss personal matters in a humiliating fashion, on live radio and for shits and giggles of all (except her).
Zangi: Pity, but it's how the law works. If there isn't an injured party, no investigation takes place. The important things to remember are that personal relationships can be incredibly messy things and that we know nothing about what actually went in in that regard. Maybe it was a case of her saying something that was only technically true, to humiliate her mother back, maybe it was someone she cares about etc. If she insists to the police that there's no need for an investigation, then it's probably best that the courts leave it alone lest they set any precedents that come back to bite everyone in the ass later.