Education is not the problem. I live in Mississippi, and can attest that we are bombarded daily with messages about obesity, diet, and exercise.
I am as educated as anyone on the mainstream teaching on this subject, yet I am clinically obese (though not for much longer).
I was poor as a child, so I think I can speak to this subject a little. It's anecdotal, but when accompanied by what I have learned from different sources (in particular, Good Calories, Bad Calories by Gary Taubes), I suspect that my experience was typical.
Poor people eat an unhealthy diet because they cannot afford high quality protein and complex carbohydrates on a consistent basis. Further, parents in poor families often work excessive hours, and quick meals become the norm due to the lack of time.
This leads to an excessive consumption of refined carbohydrates, creating an insulin imbalance that increases hunger. One of the worst offenders in this category is soft drinks. White bread is another big problem. A coke and a peanut butter and jelly sandwich was a common meal around my house.
Sweet tea is another big offender. I have rarely seen sweet tea outside of the southeast, and almost everyone drinks it here. If you order tea in a restaurant, you are getting sweet tea unless you specifically request unsweetened.
Surely this enviroment is bad for adults, but I think it is particularly damaging for children. Kids that grow up with an excess of blood sugar and elevated insulin are headed for metabolic syndrome and Type II diabetes.
Make no mistake about it, it is insulin that controls fat storage. When your serum insulin is high, your body is storing fat. When it is low, you are converting fat stores to energy. No endocrinologist or reputable doctor anywhere will dispute this fact. Nutritionists are often unaware, resorting to the calories in - calories out causation fallacy.
When you eat lots of sugar and refined carbohydrates, your insulin is going to rise, and you are going to store fat. The worst part is that modern day nutritional education eschews fat and, to a smaller degree protein, in favor of carbohydrates, so the "educated" individual is really in no better position to regulate his endocrine system via diet and exercise.