The Atkins diet worked on the premise that the body mechanism that triggered fat storage and burned fat (ketosis?) relied only on the level of carbs ingested. So a diet high in meat and other proteins (and some fat) but low in carbohydrates caused the body to believe it was starving and burn stored fat. So essentially it was a diet of meats, eggs, cheese, lower-carb veggies like broccolli, lettuce, celery, etc. Of course, if you insist on pigging out, you may actually not lose weight this way.
Similarly, by this same logic, sugar was better than starches (complex carbs) because it came and went through your system in a faster time, while complex carbs encouraged higher insulin levels for longer times. Atkins, IIRC, considered insulin the agent that encouraged the storage of carbs as body fat.
The maroon in Supersize Me insisted on pigging out on 5000 to 7000 calories a day. The fact that before this he was a thin vegetarian before this did not help his health. If you eat nice balanced meals at that calorie level, you will still gain weight and have health problems. McD’s had nothing to do with it, except he insisted on eating too much.