Except that fats inevitably have to be stored as fat droplets before they can be burned as fatty acids. This advice isn't for fitness guys or physique trainees. This is for bodybuilders who are serious about losing fat without losing the muscle. The muscle needs carbs and protein for steady energy and anabolic activity. Therefore, bodybuilding is about getting into a caloric deficit without reducing those two aspects.
Cutting carbs down too low or to none isn't an option if you wish to keep all of your hard-earned muscle before a contest. So, fats naturally must be cut- especially saturated fats since they are harder to burn and will always be stored as bodyfat first. Not to mention that people in Lee's level of competition are using steroids, GH and possibly insulin. All of these combined allows one to easily get super lean with a high carb/low fat diet.
There is ssssoooooo much more to low fat diets than the typical 80's bodybuilding gospel. There are other things to consider, such as white fat vs. brown fat, saturated fat vs unsaturated, and TEF values of fat compared to carbs and protein and how that affects metabolism. Low fat diets work, man. This notion of "all fats are healthy" may have some truth to it but that fad has only been around 10-15 years, starting with Atkins and Keto diets which have now morphed into backloading and Paleo.