Gee, where did you get that idea? It's a complete rubbish. It's the intensity that determines the ratio of fat:sugar you burn from the workout. Lower the intensity is, the more fat you burn, and vice versa.
And you don't have to burn fat to lose weight. As others have already said, you just have to expend more energy than you eat.
That said, however, I find it easier to lose weight through low intensity workouts because you have to replenish muscle/liver glycogen by eating carbohydrate after high intensity training, and theoretically you can still lose weight that way, it's harder to eat just enough carbo to replenish the lost glycogen store so that you can maintain the intensity of your workout but you don't have excess carbo that is resynthesized and stored as body fat. IOW, I easily overeat.
So, if my main objective was to lose weight, I'd do by combining low intensity (L2-L3) rides with reduced caloric intake.