A living body can be quite clever, it can change your BMR (what you assumed was a deficit is now a surplus) perform muscle catabolism, or burn glycogen stores (more than one kind of fuel) during starvation. All the while taking pains to store away the calories you do intake as new fat cells. It's precisely this kind of direct and overly simple appeal to thermodynamics that the article tries to address.

Burning fuel in a calorimeter is not the same thing as a human body. /Fat/ loss and creation aren't the body's /only/ response to calorie deficits and excesses. You can create new /fat/ cells while still losing energy and mass overall without violating thermodynamics. As I said above, all you need to do is have your metabolism prefer your other stores first.