I'm not sure the complaint about the MED questionnaire calls the study itself into question.
The study followed people who did follow randomized selection criteria in earlier studies, so the initial weight loss and fat loss did come out of a randomized protocol. Then, years later, they showed that those original random selections did have long lasting effects in visceral fat deposits, even for those who gained all their weight back. So far, we've got evidence that randomized interventions work at reducing visceral fat, which strongly suggests causation.
Then, they showed correlations between low visceral fat and other cognitive effects, and brain scan effects, suggesting causation there, too.
They did mention that they used the MED score in multivariate analysis, but didn't try to make any particular casual or even correlative link with that MED variable itself. They just put it in so that MED scores didn't show up as a confounding variable.
In other words: reducing visceral fat is good for the brain, and we're pretty sure there's causation here. Looking at people's self reported diets did not disrupt that core finding.