The information about not eating after a workout is completely wrong. Every responsible source in bodybuilding and athletics recommends that you eat after training, and preferably within 45 minutes (maybe up to 60) after a workout. This period, known as the golden hour, is when the muscles absorb the most nutrients and when glycogen, an energy reserve in your muscles, is replaced most efficiently. The actual composition of the post-workout meal is a matter of some debate; for optimal glycogen replacement, most people recommend carbohydrates, but a certain amount of protein (at least 10 percent of the meal) is needed for muscle repair and growth.
I think the above recommendation is a good general guideline for athletes, but for weight management you probably have to go higher in protein and lower in carbs. You don’t have to eat a big meal, but you should eat something after training. Lots of people get good results with a small, high-protein shake — just beware of the extremely high sugar and carb content of juice-based smoothies. Experiment with the amount of food or drink and with the proportions of carbs, protein and fat to find out what works best for you.
Perhaps what the trainers at your gym are trying to emphasize is the need to moderate carbohydrate intake in a weight-loss program. They correctly want to see you become a “better butter burner,” that is, someone whose metabolism burns fat faster and more efficiently. That is best accomplished by eating a nutritionally dense, low-calorie diet that offers a balance of protein, high-quality fat and the right kind of carbohydrates. This will keep your hormones balanced and your fat-burning machinery working optimally. I agree that you shouldn’t load up on carbs and fat after a workout, but the idea of not eating anything at all for two hours after working out is balderdash.