FWIW this response is an appeal to authority.
I was in a closely related field, and I'm familiar with the work of Cosmides, Tooby, Pinker and a few others. I also knew their students and saw how the sausage is made.
In my experience, Wilson is right. Many of these labs were not doing science. They were doing advocacy, and it showed in the way they designed studies and shelved data.
Not long after I was in school, major labs pushing this approach at Harvard and Yale had major data manipulation scandals.
Independently of this, they also had an animus against statistics that I don't think is befitting of an empirical science.
I haven't read the Wilson, Nowak, and Tarnita paper so I can't comment on it.
But from what I saw of this camp, I would be very skeptical of an appeal to authority.