The abstract of the paper made it clear that attrition was high in both groups -- neither cohort could maintain their diets. Also, you're doing a fair amount of selective quoting. From the abstract, right before the part you quoted:

"There were no differences in weight, body composition, or bone mineral density between the groups at any time point."

In other words: neither group lost more weight than the other, at any time point. Which was the OP's point. Also, the following papers were trivial to find:

http://www.ncbi.nlm.nih.gov/pubmed/15148064

"Participants on a low-carbohydrate diet had more favorable overall outcomes at 1 year than did those on a conventional diet. Weight loss was similar between groups, but effects on atherogenic dyslipidemia and glycemic control were still more favorable with a low-carbohydrate diet after adjustment for differences in weight loss."

http://www.ncbi.nlm.nih.gov/pubmed/16476868

"After 6 months, individuals assigned to low-carbohydrate diets had lost more weight than individuals randomized to low-fat diets....This difference was no longer obvious after 12 months....Triglyceride and high-density lipoprotein cholesterol values changed more favorably in individuals assigned to low-carbohydrate diets....but total cholesterol and low-density lipoprotein cholesterol values changed more favorably in individuals assigned to low-fat diets"

http://www.ncbi.nlm.nih.gov/pubmed/12684364

"There is insufficient evidence to make recommendations for or against the use of low-carbohydrate diets, particularly among participants older than age 50 years, for use longer than 90 days, or for diets of 20 g/d or less of carbohydrates. Among the published studies, participant weight loss while using low-carbohydrate diets was principally associated with decreased caloric intake and increased diet duration but not with reduced carbohydrate content."

http://www.ncbi.nlm.nih.gov/pubmed/17507345

"Variability in dietary weight loss trials may be partially attributable to differences in hormonal response. Reducing glycemic load may be especially important to achieve weight loss among individuals with high insulin secretion. Regardless of insulin secretion, a low-glycemic load diet has beneficial effects on high-density lipoprotein cholesterol and triglyceride concentrations but not on low-density lipoprotein cholesterol concentration."

Confused? You should be. What a quick perusal of the evidence tells me is that a) despite what you may have read on the internet, the question is far from settled, and b) if there is any conclusion to be made, it's that low-carb diets may have some positive benefit on cholesterol and triglyceride levels, but don't seem to have any net benefit when it comes to weight control.