The trouble with this line of thinking is two-fold, though in both ways it could potentially cut out all attempts at satire.
Firstly, whilst the story certainly could not have been written without the earthquake and tsunami, that does not mean that it is making light of them. It is quite obviously about self-centred consumerists. I was amazed - but perhaps I shouldn't have been - to find out that there really have been threads on other sites along the lines that Charlie Brooker, whoops sorry Dark Bill, is satirising here.
You could legitimately say 'OK but it's still too soon' and I'd have some sympathy, illogical and subjective though that way of looking at it is. Unfortunately, in the age of instant communication, you're fighting a losing battle. And it's pointless trying to be the arbiter of what is and isn't funny.
Secondly, almost any satirical story is going to offend someone. There have been loads of send-ups of Al-Qaeda here, including some by me (vizt. 'Al-Qaeda to postpone terror attacks until after end of Strictly and X-Factor'). Would anyone who had lost a relative to Al-Qaeda terrorism find that funny? I doubt it. Do I find what Al-Qaeda actually does funny? No, of course not. As far as I know, no-one was mortally offended by that particular sub, but you could equally well do away with it and many others on the same basis.
There's also an element of parochialism creeping in, along the lines of 'well it's OK for the Daily Mash, but not for NewsBiscuit'. Why? Is NewsBiscuit meant to be the PC satirical news website. That's, er, news to me.