1. In this one particular study, caloric restriction diets were explicitly calorically restricted.
2. In this one particular study, low-carbohydrate diets were not explicitly calorically restricted.
3. Weight loss was similar for both groups, but we assume that the Atkins fatties were gorging themselves on meat while the other people were not.
But, the data from this study was self-reported. To me, this is an immediate red-flag. It's two large waving red-flags for the inference the author is trying to engage in. He's basing a huge article on an assumption which is absent from data. This is anomaly hunting, plain and simple. The author obviously has a preconceived desire to support carb-limiting as the Deep Secret of weight loss, and so any anomaly is cast into evidence for this desire.
This is not to say the author is wrong, I'm simply saying his logic doesn't hold and analysis falls apart as a result. It's at least as basic a concept to science as the notion of control that the article leads with: "You cannot draw strong conclusions in an absence of data."
P.S., I'm not inclined to believe this good-calories-bad-calories stuff. I lost 100lbs over the course of 13 months, and I didn't do it by carb cutting.