It's a little telling that a bunch of their most lurid examples from the main text turn out to have been rejected; they seem to want to spin a narrative from the nice things reviewers said in the process of rejecting those papers. For instance, the "Masturbation" paper wasn't even "reject and resubmit"; it was a straight reject. If you don't read all the way to the end, you can miss that fact easily.

(Amusingly, they also print quotes from the same reviewer twice on that paper, creating the impression that multiple reviewers responded positively to it; I'm not going to take the time to audit all their peer quotes, but I'll bet that's a trick they applied repeatedly.)

Another example: Hypatia is apparently quite well known in feminist studies. The authors got a paper accepted in Hypatia. The authors also suggested that Hypatia was "surprisingly warm" to a paper (actually, it turns out, an essay) that suggested that white men be forced to sit on the floor in chains in classrooms. What the write-up doesn't tell you is that that's not the paper Hypatia accepted; they accepted a much more banal paper about the legitimacy of academic hoaxes.

Another example: they highlight (and so does their press coverage) a paper that spins a section of Mein Kampf into a critical race/gender theory argument. What they don't say up front is that they tried this three times, once with a relatively serious journal, once with a journal with an impact factor of 1.1, and finally with a 0.8. It's the 0.8 that accepted them; the others rejected. In fact, academic science --- STEM included --- is littered with bullshit journals, but generating that fact as the result of their "experiment" wouldn't have made for such an interesting story.

Kieran Healy makes an interesting point about this on Twitter: it's probably easier to get totally fake papers accepted than real ones. Recall Matt Might's cartoon essay about PhD theses and the tiny dent any one paper makes at the boundary of a science. If you aren't constrained by reality, it's easy to generate a paper that seems impactful. Meanwhile, the whole enterprise of peer review relies on good faith: reviewers are donating their time, and for every paper published, there are many many more that had to be read and rejected.