Earlier quoted context omitted.
You haven't read the original paper, don't even understand the methodology they used to reach their conclusions and yet you "can't help but feel this research makes pretty poor use of statistics and logic"? It seems something is bad here, but I don't think it's the nutritional research. If you can't be bothered to actually read the paper, why do you think you're able to critique it?
Cos it doesn't work with an explanation. Science is about explaining things.
Science first finds unlikely or unexpected correlations, unlikely or unexpected measurements, and seeks to understand from whence they came. Are they artifacts of the observation process? Tainting of the measurement process? Or spurious correlations, such as the one between height and spelling ability (both of which are strongly correlated with age, up to a certain point)?
This particular research announces an unexpected correlation and goes to pains to show that it is real, and not spurious. This is the observation phase, the oh, didn't expect that phase. Explanation will come later, likely after someone designs a more accurate and precise experiment to better correlate chocolate consumption and cognitive ability.