The truth is, it's all about calories in vs. calories out. I always suggest eating something before working out, even something small because you've already been fasting for 6-8 hours while you were sleeping. Whether you feel hungry or not, your body is craving fuel. Even an apple, for example, may help get you going. It contains some simple carbs which will be broken down quickly to provide a little boost of energy plus some fiber and other nutrients. Some people may even need more fuel than what is stored in order to get through an intense workout properly. The ratios of what you've been eating in the previous days along with physical activity and other factors may play a part in that.
The logic behind not eating prior to a workout usually refers to first thing in the morning. The idea, as already mentioned, is that you will burn primarily from your fuel stores (stored carbs and fat for example). The intensity of your exercise may also play a role, however, in which is predominately used. Lower intensity exercises tend to utilize more energy from fat, although the total number of calories may not be very high. Higher intensity exercises tend to utilize carbohydrates more, but usually result in a higher total number of calories burned.
At the end of the day, end of the week it all comes down to the questions, "Does a calorie deficit exist (meaning did you burn more calories than you consumed)?" As long as you have a daily/weekly caloric deficit you will be burning fat and losing weight.
In the end, the choice is yours, but personally I always recommend at least a little something prior to exercise in the morning. Remember to wait a bit after eating though before you exercise.