Like with any observational study, it's worthwhile to think of other things people who eat a Western-style diet might do differently from the control population

Like with any observational study, it's worthwhile to think of other things people who eat a Western-style diet might do differently from the control population before accepting the implication that the observed difference in memory performance is because of the food. For example, perhaps affinity for snack food has something to do with how much time people spend engaging in sedentary activities like watching TV. There's already plenty of existing evidence (mostly also observational, mind) suggesting that lack of physical activity is associated with poorer cognitive outcomes.