We analysed data on 414 societies from 30 world regions, using 51 measures of social complexity and four measures of supernatural enforcement of moral norms to get to the bottom of the matter.
This is where research of this ilk loses me. Looking at the measures of "social complexity," it's attempting to systematize specific aspects of a society. But it's not clear, even after checking out the study that it's based upon, how this actually works. They seem to be saying that certain things correlate with a more "complex" society, but it's more that they're defining what a complex society is and then saying that certain factors make this so.
That this never happened in all of the Americas, for example, makes me question how universal this truly is. They also do not sample any religions that cropped up in the southern 2/3s of Africa.