I think the difference is between the diet people around the mediterranean used to eat and what they eat now.
When we went to Majorca self catering over 30 years ago, we went virtually vegetarian. There were markets piled up with beautiful fruit and veg and the fish also was good, but expensive. The meat was not, which was why we lived, very well on vegetables, peas and beans, rice and pasta. DH's aunt was married to a majorquain and her meals were also the traditional idea of a mediterranean diet.
We are currently on holiday in Spain staying in a hotel. The meat, cooked and cold, is still unappetising, and anaemic sliced processed cheese has replaced local cheeses. I am not eating it. The fish is good, but meals are accompanied by rice, potatoes, pasta with very little in the way of additional vegetables. I cannot wait to get home and get back to my usual consumption of fruit and vegetables.
I do not think it is the advice about eating a mediterranean diet is wrong, it is just that people in countries around the mediterranean no longer eat it.