Globalization intensified competitiveness among agribusinesses worldwide in recent years. The European Commission focused on enhancing sustainable agriculture and food products’ territorial uniqueness for competing in the international market. The Mediterranean diet (MD) is a model of feeding and lifestyle belonging to the ancient Mediterranean culture, which also embodies a sustainable food system. Therefore, in 2010, UNESCO recognized the MD as Intangible Cultural Heritage of Humanity, and Sicily (southern Italy) is its official physical site. Despite its worldwide fame, the notion of the MD runs the risk of being mystified because it is described most often as something that does not correspond to what it is holistically. The aim of this study is to know the market demand of the MD by Italian people and foreign tourists in Sicily and the level of knowledge of the MD by users, both consumers and experts. A survey at top Sicilian traditional restaurants with owners/chefs and their clients was carried out. The study provided an in-depth understanding of the current lack of knowledge about the holistic meaning of the MD. The study highlights the desirability of integrated science–policy actions (also for communication) and proposes a vertical communication system to revive and direct the MD demand toward its holistic model.