This belief is partly based on a gross and blatantly incorrect interpretation of research concerning TEF (Thermic Effect of Food).
The problem here is that the research has been presented in such a way that it has lead people to believe that the net effect of TEF of several small meals would be greater than that of a few, large meals.
TEF is directly proportional to the calories contained in the meal you just ate (ref). Assuming a diet of 2400 calories, with the same macronutrient composition, eating six small meals of 400 calories or three big meals of 800 calories, TEF will be exactly the same at the end of the day.