The New York Times just wrote a piece on the proliferation of fake academia - what is essentially "fraudulent" journals and conferences. Here is an excerpt from NYT:
OMICS International is a leader in the growing business of academic publication fraud. It has created scores of "journals" that mimic the look and feel of traditional scholarly publications, but without the integrity. OMICS is also in the less well-known business of what might be called conference fraud. Both schemes exploit a fundamental weakness of modern higher education: Academics need to publish in order to advance professionally, get better jobs or secure tenure. Even within the halls of respectable academia, the difference between legitimate and fake publications and conferences is far blurrier than scholars would like to admit."
But fake think tanks have been around awhile. Here is a piece that Think Tank Watch wrote in 2015 about "fake" think tanks.
In fact, fake think tanks have been around for decades. Take the so-called Boring Institute, a "fake," one-man think tank that originated in 1984. Here is more on that "think tank" from the New York Times.
We should also note that there are a number of fictitious think tanks floating around...
Update: Here is a new Wired piece entitled "Fake Think Tanks Fuel Fake News - and the President's Tweets."