WAT
This is wrong.
When I spent a month in Greece, I had practically no grain except restaurant bread. A bit of pasta once. It's a lot of seafood (mainly fish, a bit of octopus), vegetables, olive oil, meat, some dairy, a bit of grain. Oh, and a glass of alcohol. Meat monthly? That's crazy.
Grain was really not high at ALL on the list of things consumed, in fact in the meals themselves it was pretty much non-existent outside of occasional pasta/moussaka/etc.