Not true, some diets raise metabolism relative to others according to recent studies, low carb diets burn about 430 more calories on average per day for the same level of activity. So that's another way of burning calories without "exercise" unless you consider sitting still exercise.

But that's precisely what this article argues is a falacy. He discusses a trial carried out in hospital conditions with regulated liquid meals of exactly the same number calories but differing carbs/ protein ratios. The results showed that given the same calories and exercise all the subjects maintained the same weight.

Unless I misunderstood anything.