I've lost 75 lbs over the last 18 months by simply limiting all carbs as much as practical so my inclination is to not attribute the weight loss to a specific type of carb reduction. But it would be interesting to control for different types of carbs to test your hypothesis.
I'm pretty sure you lost weight by reducing number of calories.
For example, consuming 2000kcal of refined sugar and 2000kcal of beans will result in different calories absorbed given that 2000kcal of beans requires much more energy to digest than sugar liquid.
