When someone says “carb restriction is the ticket,” they’re attributing the effectiveness -to the carb restriction-, explicitly, as having an effect on weight loss notably above and beyond that of calorie restriction.
Pretty much no decently structured studies have supported that. A couple animal studies suggest shit like HFCS has a much more severe short term effect on insulin than other foods, but they’re small, animal based, and “don’t eat junk food” is world away from “carb restrict.”