I am currently on the Southbeach Diet and losing weight.
It is very easy to say everyone (99% according to the article) who is fat is just a pig. The truth is that it’s more complicated than that.
A lot depends on what you eat. For me, cutting out processed foods did the trick. You also have to increase your fiber intake and eat a reasonable amount of fat - both of these help you feel fuller for a longer period of time.
Fat is energy. If you're expending as much or more than what you consume, and still not losing weight, then either you were not doing the amount of exercise required to lose weight, in relation to the amount of calories replenished/stored in the body, or your measurements for the calorie content of the foods consumed were wrong. If neither, your body is bending the laws of physics and creating energy out of nothing, which is quite unlikely.
That thing about walking 20-mins briskly everyday to lose weight is just BS, especially considering the richness of the modern diet. Running 5-8 miles a day, every single day, would do wonders to achieve fat loss, provided it is not replenished at a rate greater than the body's ability to store food as fat, and the length of the run depending on how much fat there is, to burn. Weight training allows muscle growth, through microtrauma on existing muscles, that help in burning calories even while resting, thus enabling one to "keep" the weight-reduced state for longer.