That may not actually be so.
Your body is a very clever energy storing and making machine. It engages different processes, depending on the demands made upon it.
There is a certain amount of energy that your body needs, just in order to exist and function. This is your base metabolism rate (BMR)
The next level of effort is the fat burning stages. When you exert your body above the normal daily existence level of effort, this is the fat burning zone. If you imagine it to be the level of effort that is just a little bit out of breath, but still ok, and you could go at this level for a couple of hours. Your heart rate will be moderately elevated. A steady continuous level of effort for an hour upwards.
If you are working pretty hard, to the level where you are gasping for breath, can only talk in short phrases, heart rate very elevated, this is anaerobic. The body’s fat stores are for slow continuous energy, and this level is far too high for that type of fuel to be used. Therefore your body will use your carb stores, which are glycogen stores in your muscles and liver, and the carbs you ate today. It bypasses the fat stores at this level.
If you are trying to exercise for fat loss, then the answer is yes. If you are working your own butt off each time you visit the gym then perhaps you need to lay off a little, and get into the fat burning aerobic level of effort. This type of exercise needs to be sustained though, so 30 minutes here and there would not be sufficient for fat loss. Try and make it an hour of sustained effort, more if possible, for a better result. You would get better results from a couple of good long sessions a week rather than some regular 20-30 minute sessions.
Also, to compliment that, increase your muscle mass through lifting weights in the gym. Weight training increases your fitness, which in turn increases your metabolism. A higher (more effective) metabolism in effect means your body is more effective at burning excess fat. For more, read this recent blog dealing with the myth that weights make you fatter in the long run.
Be patient in the transition period towards your new body, and measure success through inch loss, you will get a much more favourable measure of your progress.