Although I agree that mathematics (specially statistics) is often abused in social sciences to obtain results that should not resist critical review - from assuming stronger results than the maths actually show, failing to apply consistent methodology (for example not controlling variable dependency) or just plain non-sequiturs, I think the effect described here is not so much concerned with mathematics itself as with confidence on competence.
When someone requests a service, especially a knowledge service, there is an implicit trust in the intellectual honesty of the provider - if I request legal counseling, I do not expect that the service provider will behave in an incompetent fashion. If he cites bogus laws, how can I detect it unless I am a legal expert myself? When the social scientist sees a paper with a mathematical model, if he does not truly understand it, he at least makes the assumption of competence from the writer. Since a mathematical model usually provides a non-ambiguous problem description, the presence of one usually does imply greater rigor - at least to the extent that other scientists can reproduce and test the model. In that way, the social scientist is making what I think is a reasonable decision when prefering papers that have underlying mathematical models, at least to the extent that the underlying experiment usually will be more reproducible.
What does this say about review processes? I think the only lesson we can take from this experiment is that papers should be peer reviewed and rated by those with competence to understand the entirety of the paper. If a reviewer is uncomfortable with the maths, he should consult another expert that can help him in that regard - no one can be burdened with the duty to know everything.