For weight loss to occur one must burn more calories than they consume. In a deficit the calories will come ultimately from fat. If you eat more calories than you burn you will gain fat. During low-intensity training a higher percent of fat is burned. During high-intensity training a higher percent of carbs (glycogen) is burned.
As a percentage this is true. However, high-intensity training will burn more calories and fat overall when compared to low-intensity training.
Lower intensity training will burn 70% of calories from fat while higher intensity training will burn 50%. If you work out for 20 minutes, you will burn 100 calories at a low intensity and 200 calories at a high intensity. Would you rather burn 70% of 100 or 50% of 200? High-intensity training also improves your V02 max, which improves your fitness level. This does not improve with low-intensity training.
While not everyone is capable of doing high-intensity training due to their fitness level, age, injury etc. doing small intervals at a higher than your usual intensity will help develop the ability to work out longer at this higher level. Having said that for some individuals low-intensity, longer workouts are still their best option for safe effective exercise. Those individuals that have the ability to safely workout at a higher intensity should kick it up a notch and enjoy the added fitness benefits.