Anyone can lose weight simply reducing calories, but that weight loss isn't permanent or sustainable, and it may not be healthy. If you run the numbers, the Twinkie Diet guy was actually eating fewer carbs than the average American simply because of calorie restriction, and his low protein intake would almost certainly result in the loss of muscle mass.
The age old advice of "eat less, move more" ignores the body's natural mechanism for fat regulation, which is primarily the hormone insulin. The higher your blood glucose, the more insulin your body produces, the more fat your body will store, and the less reluctant it will be to release its stored energy.
It's obvious that if you're eating fewer calories, then less energy is available for fat storage -- it's simple thermodynamics -- but basic endocrinology tells us that to lose weight all we need is the negative stimulus of insulin, which is primarily achieved through reducing carbohydrate intake.