FWIW, I don't find their treatment of reverse causality convincing. Adoption of Confucianism as a predictor of peasant revolts is as plausible as their preferred causal arrow, and in some cases makes better sense (eg they seem to think of temples as brainwashing nearby subjects, but AFAIK most temples were not 100% state-funded and rely on contributions... so temples are more plausibly a measure of Confucianism, than a cause of Confucianism; and given how explicit Confucianism is about being a tool of central state propaganda & control, would it be at all surprising if more independent places aren't too keen on it?).

They try to use a measure of 'Confucian sages' a millennium before to deal with this a bit, except that measure is from the same data source as everything else, which was compiled in the 1890s.