You know, if I was a global brand like the NYT or Twitter and the same group kept screwing with me I would hire people to deal with the issue. Waiting (hoping?) for the Anonymous nutters to do something just seems like a terrible, but potentially hilarious, accident waiting to happen. They're lucky all they got was a few dick pics and apparently a turd, with Anonymous it could have been an infinitely more varied and awful bunch of images.
Anyway, there are legitimate entities with far more experience and better equipment who you can pay to track down and identify bad guys. They should get someone like that to deal with the problem.
Hell, if I was a multimillion dollar corporation whose existence depended on me keeping up a robust image I'd probably be considering Congolese mercenaries.