Because she's deeeead
Ok, the BBC article doesn't state, but heavily implies, that the prank call was what led to the death. It's now apparently generally thought to have been suicide (and whether that's actually been reported anywhere or it's a case of mass public assumption I don't know, but the hospital man's quote in the article seems to lead to that conclusion). What I'm objecting to is this girl holding the DJs responsible for the death, when what they actually did was put on silly accents and make a prank call on their radio show. Whether it's an indirect cause or not, they're in no way morally responsible because it's very clearly not a careless act of public endangerment. The worst thing they're guilty of is wasting airtime with weak filler material.
If we really, desperately need to blame someone (and, needless to say, we do), we'd do better to blame the desperate journalists who reported on this 'story' with enough excitement to convince the lady that she'd severely compromised national security through an act of unforgivable negligence. Not that it's their fault either of course, because there's no way anybody could have predicted that she may have been particularly vulnerable. What it actually is is a shame, and nothing else. Neither malicious nor reckless on the part of anyone involved.
The DJs, predictably, have lost their jobs, and the hospital have 'received advice that what the Australian broadcasters did may well have broken the law'. To me, that sounds like 'they haven't done anything that's clearly wrong, but we might be able to punish them for something'. So we're deciding to punish, then scouting round for an excuse. In that situation, can we not just admit that they're not at fault? Losing one's job is already a pretty harsh punishment for nothing. But I guess they also committed the crime of making a prank call to the UK relatively soon after another radio prank call in the UK had gone wrong on a slow news week, so it is now maybe uh first degree murder and arson? I'm not sure exactly how the trial-by-Facebook method works.