Except the Mayo Clinic and the CDC is wrong. You can lose weight eating high fat/high calories AS LONG AS YOU KEEP CARBS LOW. I have a friend who lost 50 pounds eating this as his normal meal:
Breakfast: 3 eggs (all with yolk) and 4 pieces of bacon (or sausage)
Lunch: 2 Burger patties (without bun), 2 pieces of cheese on it, maybe some salad
Snack: Nuts, Cheese
Dinner: A big ass steak and some cooked vegetables.
Keepking blood sugar low/insulin low is much more important.
Look at the people who lost lots of weight eating 'bad' fatty food:
http://www.reddit.com/r/keto
The 'low calorie' myth is an oversimplistic explanation because it's much easier to tell people to eat less calories rather than focus more on the TYPES of calories you're eating.