The whole idea behind exercise from a weight loss perspective is to burn extra calories. If you're having trouble losing anything though, it's often beneficial to do exercise first thing in the morning. The idea is that your blood sugar is bottomed out. Your carb stores in your liver have been depleted overnight. So basically, when you exercise in this state, you almost immediately start pulling energy from fat, as your body has no other choice, there's nothing in your bloodstream to burn.
As for the above car analogy, sure, that's right from a performance perspective, especially strength training. BUT, from a weight loss perspective, the idea would be that your "car" has a reserve tank (fat) and you're trying to burn the gas in THAT tank.
So basically the analogy would be more like, you have a race car, and you're trying to make it lose weight so you can go faster. You've got the basics, and even have a small 1-2 gallon fuel cell to save weight on gas, which is full of high octane fuel (your carb stores). But, you're overlooking this 100 gallon reserve tank, which is full of cheap low octane fuel (fat). This tank is connected in such a manner that your car won't burn gas from it until the fuel cell is out, and if you start on high octane then immediately try to switch over to low octane in the reserve, there is a switchover period and your car doesn't run too well during that time. Without siphoning the gas or major mechanical work (surgery), the best way to lose the pounds from that gas is to burn through your fuel cell, then let your car putter around and burn off the reserve tank, right? So with that in mind, if that's the goal, do you think it would be easier to fill up that high octane fuel cell every time you drove your car, burning that good fuel first then having an awkward switchover period, assuming you even GET to the stage that you have to switch over, or do you think it would be easier to just take off with an empty fuel cell and start burning your reserve tank immediately? Just remember that even then you're burning cheap low octane fuel in a prized race car, so you have to be careful and not try to drag race during this time, take it easy, and limit the intensity.
Same exact thing with your body. If you start with no carb stores in your liver then do medium intensity cardio that works your slow twitch muscles, you'll be pulling your energy from fat, which is exactly what you want to do from a weight loss perspective. Just don't strain yourself. Straining, strength training, etc., uses fast twitch muscles, and you will have no fuel for them to use. This is why you would feel light headed. Your blood sugar would already be low enough, don't abruptly do anything that would bottom it out even more, it could get dangerous.