The theory that people will be healthier by decreasing fat and increasing carbs has led to our current obesity epidemic. I would classify the science performed that got us to this point as fulfilling your requiremen.
Nutrition is an especially crude science with nothing approaching scientific theory, and a lot of disagreement. FDA recommendations like the food pyramid that recommend altering fats/carbs are the result of political consensus as much as science, and there are many counter-examples to the idea of high carbs / low fats in the diets of different peoples of the world.
What evidence was that theory based on?
None. Much like the new dietary guidelines, it was based on politics, lobbying, and bribery most likely. Nutrition is inherently difficult to study, and hasn't really been taken seriously until recently.