Data from epidemiological studies is so weak as to be almost worthless.
According to Dr. John Ioannidis the conclusions reached from observational studies are wrong 80% of the time. So unless there is a randomized trial that also supports the hypothesis it is more likely than not that the conclusions of the authors of this study are wrong.
In fact, you shouldn't conclude anything from epidemiological studies. They are hypothesis generating studies that should give you an idea of what kinds of interventions you should investigate in a real scientific study.
Here are some randomized trials:
Compared with a low-fat diet, a low-carbohydrate diet program had better participant retention and greater weight loss. During active weight loss, serum triglyceride levels decreased more and high-density lipoprotein cholesterol level increased more with the low-carbohydrate diet than with the low-fat diet.
In addition, the low-carbohydrate group lost less lean body mass:
...Patients in both groups lost substantially more fat mass (change, -9.4 kg with the low-carbohydrate diet
This seems like an authoritative 25-year research project that the Atkins diet is pretty bad:
http://www.nutritionj.com/content/11/1/40/abstract
Right now my belief is that the Atkins diet is good. It's backed by anecdotal evidence of trying a low-carb diet for 18 months following a 12-month low-fat diet and seemingly getting better results with the low-carb diet.
I'm counting on LWers to tell me how to update my belief in light of this study. Thanks.