This is correlation on a self selected group. A different statistical correction is needed for those. (These people are not being fed this diet despite their wishes, so there are lifestyle, metal health and other correlates.)

Thus causality can go either way with multiple factors interfering. The experiment is not powered enough to actually derive a conclusion. They'd need at least a 2 million sample sizes for each group to show anything other than noise, and that's with the ultra fancy multilinear math used in genetics to untangle multiple factors. (Advanced variants of FAMD.)

Welcome to land of observational studies.