This should be one of those things that is really obvious. People are always looking for the magic pill, or that certain thing to add to their diet to lose weight, but the simple truth is that the only way to lose weight is to expend more calories than you take in...
I think most people tend to overestimate how much they burn via exercise which makes it seem like it's ok to eat more or the same and expect that they will lose weight.
This is absolutely true. (Calories in)-(calories out)= net calories. If you want to lose weight, the final product should be negative, if you want to gain weight, it should be positive. If you want to lose or gain more quickly, the number should be MORE negative or MORE positive. Pretty simple. In addition to your point that people always want to add a certain thing to their diet, equally so do they want a magic "bad guy" to take out of their diet. Fats, Carbs, HFCS, GMO's, etc. All have been blamed, at one time or another, for our overweight population, and all have been acquitted as the sole demon of our diets. It's overly-simplistic thinking, and I can't believe that we can't just teach kids the equation you noted in a school health class. Because it's not that difficult to grasp.