I've seen at least one study indicating that extra virgin olive oil (but not the more processed varieties) is associated with better health outcomes. This suggests that the health outcomes are being driven by oleocanthal, an anti-inflammatory compound in EVOO (if you've noticed a 'burn' at the back of your throat after consuming EVOO, it's from that) more than that it's monounsaturated. There still isn't a good understanding of how AD occurs, but a number of the leading hypotheses feature inflammation as at least partially to blame, so daily consumption of oleocanthal might have an effect (supposition on my part). I haven't seen anything regarding the MIND diet that mentions the type of olive oil.

BTW, based on the 'burn' at the back of my throat, 'Greek' style (early pick, usually koroneiki or arbequina varieties) typically have more oleocanthal than the more buttery-tasting 'Italian', style (picked at full ripeness). No science there, though...

Oh, and many of the EVOOs you can buy at a US supermarket are not EVOO - either they're some other grade of olive oil or adulterated with (or completely made of) some other kind of oil, probably with chlorophyl added to give it the 'right' look. Long story, google 'counterfeit extra virgin olive oil' for a possibly surprising read.