This post is extremely misleading and dangerous. Why anyone would want to propagate this lie is beyond me.
Exercise does lead to weight loss. The article cited clearly says it does. It's just that a small amount of exercise -- aerobic exercise for short periods over a mere three months, without strength training or diet changes -- is less effective than you'd want it to be. Well duh. But even in those circumstances, with all those factors stacked against weight loss, the participants still lost some weight.
A counterexample: A mildly overweight or average person, who has no heart problems and is otherwise healthy, can engage in much more vigorous exercise. An hour on the elliptical can burn approximately 700 calories. An hour in an intense gym routine can burn more (ever see those ads for LA Boxing touting the one-hour 1000 calorie workout?). Lets say you do an hour of 700-calorie cardio every morning and dont change your diet. That's an additional 3500 calories you're burning per workweek. If you give yourself weekends off and don't change your diet and don't strength train, you're still losing a pound a week, mostly of fat. If you add in proper diet -- not calorie restriction per se but just switching from soda to water or cutting out one or two greasy meals a week -- you're doing better. Add in strength training and you're be doing amazingly.
But it's not enough to just diet. The health benefits of good cardiovascular health and muscle strength are important in their own right. Things like the Hacker's Diet work to lose weight, but they are very unhealthy, even possibly dangerous. It condones a quantitative instead qualitative approach; the Hacker's Diet seems to take the position that you can eat microwave pizzas for every meal as long as you keep it under about 2000 calories. What it doesn't tell you is that in the process you'll be failing to provide muscular support for an aging skeletal system, adding cholesterol to your body, hardening your arteries, and atrophying major muscles.