There is no Mediterranean diet. It a huge collections of diets and cuisines that have at times very little in common. In the Blue Zones, a book on this topic, 2 particularly healthy medi-diets/lifestyles are examined.
You would have tomatoes from June to August. Sardines would be the fatest around July. You would have grapes and wine by September and chestnuts by early November. You would kill a pig for multiple families once a year, eat some of it fresh and salt/smoke the remaining.
Perhaps this seasonal scarcity is not a protective factor but it seems to me that this a variable that is never discussed when looking at traditional diet of <geographic-region>.
Great point. Also keep in mind that religion plays a critical role. Greece in the mid 1900's was a very religious country, and most people attended the 40 days diet that they would abstain completely from consuming land-animal products.