Sugar is the real enemy, not fat. Google Robert Lustig. BIWI posted a link to his video about obesity and he firmly believes, and has scientific evidence to back up his beliefs that sugar is evil and the cause of the obesity epidemic. He had a book out called Fat Chance. But it's all about sugar, not fat.
Eating natural fat makes you lose fat. It's a fact borne out by those of us who are low-carbing, whether we have been doing it for a week, or a year, like me. I am one of those fortunate people who's weight-loss has not been stalled by eating copious amounts of cheese. I don't drink though 
I bought a size 10 top today. Yay! It's a year today since I started this WOE. I'm a shade over 5 stones lighter than I was a year ago. I have done this by eating butter, cheese, eggs, mayo and some fatty meat ( although I have to confess to not liking the fat on meat.). I have done this by not eating anything sugary (apart from dark chocolate!). I've eaten industrial quantities of nuts. But no sugar.
I haven't done a lot of exercise although I have a very physical job which involves a lot of walking, stairs, bending, stretching, lifting and carrying.
Fat is good. Sugar is bad. It's as simple as that really.