I have to agree, based on the evidence provided that the Atkins diet does work!
The problem is that it does it by tricking the body into believing that it is starving for the first week or so. The body starts shifting the fat you store to keep up energy levels as it won't burn protein unless it really has to.
When the white fat is all burnt off the body will start burning the proteins from the diet to suppliment the low levels of carbohydrate that it is now getting (I understand that you are allowed some carbohydrate containing foods after you've been on the diet a while). The proteins are first made burnable by the liver and THIS is where the possible health risk appears. Turning proteins into a usable energy source releases some rather toxic compounds into the liver. The long term effects are not really known but some people who have been on the Atkins diet have had to stop short due to severe liver problems and even liver failure.
As a short term fix it is probably a good thing, but I certainly wouldn't like to use it for a long time.