[kragen]

I haven't read the paper, so although this response applies to your criticism, it may not apply to the paper in question.

A linear model has only two parameters, which cuts down a lot on the overfitting problem, and since it's the default thing to try, you can be reasonably sure that it isn't the product of a "garden of forking paths". More sophisticated models, such as exponential, logistic, or quadratic — which may in fact be more appropriate on theoretical grounds — can easily be the product of researchers choosing among a large number of possible models based on what the data looks like.

I do not think that your suggested approach of removing science from social sciences, reducing them to a sort of literary criticism or scholasticism, would be an improvement.