Presuming that the "information" released by the anonymous hackers wasn't planted by someone who already had that information from other hacker sources, like the CC data thefts from Target and Home Depot among others.
I know next to nothing about Josh Duggar, but I could imagine that planting false data is all in a day's work for people in the hacking business, particularly when they may also be hacking for government intelligence agencies on the side.
Of all the people to frame... you think they’d go after Josh Duggar? This is the same guy who was molesting his little sisters. Also, there’s an OKCupid account with the same email address, and he’s put his picture on it.
http://www.okcupid.com/profile/joesmithsonnwa
Not only is he guilty, but he’s incredibly stupid.