It's funny to me that the article doesn't mention the word "muscle" anywhere. It seems a diet like this would reduce muscle mass, which may be a large contributor to the decline in body weight mentioned in the study.
Not a doctor too, but from what I've read it's due to insulin. Carbs usually raise insulin, proteins can raise it too.
So this means, unfortunately, you will lose muscle while losing fat. Fortunately it is significantly more difficult to extract protein from muscle, so it responds much more slowly than fat.
The minimum seems to be about 40 g (~150 Cal) of protein per day (I don't remember where I got this number, sorry.), but can be as high as 10-30% of Calories supplied by the body.
There are a lot of things you can do to counter and minimize most this though. Working out to signal to your body the muscle mass is still in use and protein shakes (no fat, no carbs) are the most obvious.