I've always heard that the best way to burn fat is by maintaining your heart rate on one of the cardio machines. Is this true?

It is not the best way to burn fat. Having said that, aerobic exercise does help you to burn calories and does have some impact on fat metabolism. The problem is that once you stop the exercise, the additional calorie burning and fat burning stops as well. Also if you perform the high-intensity interval training the way the program has taught, you will be getting aerobic exercise at the same time that you are building muscle. Now you're getting the benefits of both and you will continue to burn fat 24 hours a day as a result of the extra muscle that you were able to put on.