I hate to disagree with everybody here, but that diet will actually work. The total amount of calories is very low. There are virtually no carbs in it, providing a low GI. The bacon in the morning is greasy, but since you won't be mixing it with carbs, your body won't store it as fat. The fat food in the morning will supress your carb cravings. Plus grapefruit is actually a usefull fatburner. There are plenty of studies done on that as well.
That being said, there are a lot of better diets out there, and this diet is in no way usefull for a BB.