I agree partially , but not entirely. if one accepts the premise ( as I do ) that the ability to lose weight is a function of how much insulin -( the fat making hormone) you have in your body, then it would seem likely that ANY diet that reduces circulating insulin quickly, will also reduce weight quickly. As such the composition of the diet IS important.
You are missing an important point, on 800 calories a day the carbs will be fully utilised quickly even if the diet is 100% carbs! Fat then gets removed from the liver within about 1week, and then at least overnight insulin will drop to a low level as BG drops a lot after the first week.
The shakes that are used for the ND results in people testing positive to ketos, proving that insulin levels must be getting low at least for a few hours each day.
“Low Carb”is very important for normal diets that tent to be closer to 1200 calories a day, as otherwise insulin may not drop enough. Very Low Calories diets are closer to fasting then to a normal diet in how the body responds.