Earlier quoted context omitted.
You are assuming that poorer means worse diet. That is simply not true at all in relation to having a healthy diet, and the opposite is perhaps true. In many places the traditional diet is healthy. Then, when people become richer they eat more, eat more meat, more fat, more sugar, more processed food, etc., and obesity and cardiovascular diseases shoot up.
As a poor person who's always been surrounded by poor people, you are wrong. Poor and less educated people know nothing about nutrition and don't have the money to buy good food. When you don't have the money you are forced to fill up with cheap calories like bread, rice, pasta, sugar, etc.
In Sicily, as that is the example given, people are poorer than the European average and significantly poorer than the American average. Yet they have a healthier diet.
The issue of unhealthy diets in the US/Europe is not so much poverty but a culture of junk food and not knowing better.