Right now, we don’t. People could use any email address.
Tied back to a valid CC charge, however, and that becomes a different story.
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.