Both the magazine and the video were right, but both only tell part of the story. I wouldn'y mind but the whole story isn't all that complicated and, if more people knew it the more people would have happier, healthier lifestyles.
Exercise alone will not necessarily lose you any weight. It does make you healthier and fitter and tones you up. This means you reduce your lifelong risk of developing a whole range of medical probelms (e.g. diabetes type 2, hypertension, lots of heart related problems). You feel better and more capable of doing whatever it is you want to do AND you will probably be smaller, even if you don't weigh any less!!!
BUT exercise DOES help you maintain any weight loss. You have to do the whole healthy lifestyle stuff, as Carrie mentioned, then regular physical activity will help to ensure that any changes are more likely to be both greater and permanent. This is probably were the 'exercise helps shift stubborn fat' bit comes from!
But this doesn't mean you should throw yourself into a calorie RESTRICTED diet. Contrary to popular belief it is possible to eat too little and this will cause your body to store MORE fat, making things worse. What you need to do is to start eating the right things in the right percentages - yes, all those 5 portions of fruit and veg, 1.5 - 2 litres of water, 65% carbohydrate, 15 % protein and 20% fat (The WLR guideline for these % is based on a consensus amongst nutritionists that a diet fairly high in carbohydrate and low in fat is best for health).
Or the food pyramid
What it boils down to is probably the least exciting advice ever given, eat according to the guidelines and do 30 mins of moderate exercise on most days of the week and you will be fit, healthy and, probably, lighter and smaller!
I hope this isn't too boring!
I am a health and exercise practitioner (I lecture at University and I'm a personal fitness trainer to people with medical conditions such as heart problems, arthritis, extreme overweight etc). I give out this kind of info onmost days and I know it is not easy to hear, or to do! But this is the right place to get loads of info and support!