Hello! Actually i have never heard of a recipe 'greek rice' in Greece; imagine, it would be like saying in Brazil 'Brazilian Steak' :). I can only imagine that it has to be a mixture of rice with vegetables. Without being 100% sure i think that rice, which in the last century is popular in Greece, has not been largely cultivated before the 20th century. The most commonly cultivated plant has been beans which used to be called the Greek 'national food'