That claim starts by being false in a trivial way: Not every kind of calorie burn is due to exercise. At a QS conference I was talking to a woman who found that if she exercises in the morning she won't move much the rest of the day. She burned the most calories when she went out shopping for a day.

In more controlled enviroments lab animals who are fed a controlled diet weigh more than they weighted decades ago. I don't think that's due to the mouse running less maces.

More importantly it's irrelevant to the empirical fact that the success of the intervention of having people attempt to diet and exercise is medicore. It's rational to chose interventions that work for other people.