Looking this over, I'd say that the controlled environment had more to do with the reported weight loss than the diet. Specifically, the observation that the people in the study lost weight on the baseline diet before going on the carbohydrate restriction.

Anecdata: I lost quite a bit of weight on a version of the low carb diet: The Specific Carbohydrate Diet. I went on it for health reasons. Specifically, I was trying to manage a digestive disease by diet. I went off the diet during an extended flare after changing physicians for treatment (my old physician left practice). The diet and the flare dropped my weight to unhealthy levels. I am now under treatment that has my symptoms under control.

I am back on the diet because my weight has gone a bit too high. I, personally, find it easier to restrict my calories by removing grain-based carbohydrates. This will vary from person to person.