Not true. Eating a low fat (and thus high carb) diet, I was running 5 miles/day, 5 days a week and still fat. Going off carbs and enjoying fat has caused a big weight loss that has stayed off for 4 years - in spite of a back injury that kept me from running for the first 3 of those 4 years.
Well c’mon, I didn’t say a person can eat an all-carb diet.