the reason it has potential to prevent weight gain in humans is due to higher proportion of Type 1 muscle fibers. These are the kind with lots of myoglobin (protein that stores extra oxygen) and carries out the highly active metabolic process known as oxidative phosphorylation. This is opposed to the Type 2 fibers wherein they must go through glycolysis as their primary form of ATP production (with lots of lactic acid metabolites).
In effect, the theory is that it doesn't matter where the glucose comes from (beit from carbohydrate sources, or from beta-oxidation of lipids), because you will be able to burn more without creating an overly acidic environment (as would occur in lactic acid production from Type 2 muscle fibers). Also keep in mind that Type 1 fibers are found in muscles that are constitutively active, such as those in postural muscles alongside the spine; which accounts for their greater endurance before fatigue.
i think the theory behind this is that glucose (from carb sources) are getting burned primarily. Then, due to the high metabolic demand of these fibers, fat must be used to feed them, which would promote lipolysis (breakdown of fat). This allows one to eat high-fat meals without the consequences of storing excess calories in adipose tissue.
And keep in mind that insulin will facilitate entry of glucose into adipocytes as well (so despite high carb diet, this is how you gain fat), so if you eat a high carb diet, it is akin (not "atkin's) to eating a high fat diet after glycogen storage granules have been maxed out in skeletal muscle and liver.