You wonder if it's mostly the weight-loss that solved the problems, and if a person loses weight by strict calorie counting, carbs or not, would it have the same effect.
Low carb diets get insulin down and ketones up. These factors are more likely to be driving these other changes.
Also, low carb diets generally eliminate wheat and therefore gluten. Gluten becomes gluteomophin, which causes it's own problems (as an opiate). The standard American diet micro-doses an opiate at every meal. What could go wrong?