Who was "at fault" for this poor nurse's death? Well, to a greater or lesser extent ...
1) The presenters who made the call
2) 2DayFM, the radio station who broadcast it - even more so than the presenters. The prank call didn't go out live, somebody senior sat and made a cold judgement to broadcast.
3) The other news media in this country and around the world who re-broadcast it. I doubt if it had stayed as a 2DayFM broadcast only that the nurse would have killed herself.
4) The society we live in, sections of which laps up such cruel pranks, which makes the media feel justified in broadcasting them.
5) The hospital - if (and only if) it didn't give any advice or training on coping with phone calls, or didn't do its utmost to support the nurse following the broadcast.
Also "fault" would be the wrong word, but the nurse herself and her family and friends obviously have a part in her death. The nurse herself, for not being strong enough to cope with the situation she found herself in, and her family and friends for not recognising that and supporting her sufficiently through it.
Chiefly at fault I would say are the people at 2DayFM who decided to broadcast the call.