"Potential limitations of our results are due to the fact that the survey was based on cross-sectional data. Therefore, no statements can be made whether the poorer health in vegetarians in our study is caused by their dietary habit or if they consume this form of diet due to their poorer health status. We cannot state whether a causal relationship exists, but describe ascertained associations"
That’s true—but most studies with findings to the contrary are based on the same limited methodology.