What specific quantitative reasons do you have to suggest a questionnaire is not appropriate for this type of study? Did I miss some other study somewhere that suggests a questionnaire can never produce good science?

Who uses a certain (previously uncommon) diet that is said to help with diabetes and other serious issues? Those who are of average good health or those who experience some issues that already start to manifest? I wonder if the study corrects for those factors. Does the average person even participate in those studies?

We really need multiple long-running (50+ years) randomized study that controls for all influence factors to really answer the questions. Something that is unlikely to be accomplished in our current political lifetime and unlikely to be completed within our lifetime.

That's how most dietarey studies are conducted, including ones contradicting this study. It's not that this kind of study is very accurate; but it's nearly impossible to conduct a study of peoples' diet that will be more accurate.