Aside from the fact that there is no, one Mediterranean diet, the major flaw in looking at one aspect of a population that lives longer than others is that the one factor you are looking at might ave little to do with it relative to other factors.
Maybe people on Crete live longer because they are on Crete--that is, maybe other environmental factors are at play, besides or in addition to diet. With an island population, one must also look at genetic factors.
This article explains the concept, albeit in a slightly different context:
As an aside, knowing the fraud that Ancel Keys was, I have no trust that the diet he and Leland Allbaugh concocted was actually eaten anywhere on the island...