Exercise is still a good way to drop in weight, but not simply due to burning up the fat; that could happen anyway. What seems to be happening is that the exercise improves the body's budgeting logic, probably by putting you back in a regime evolution already dealt with.

The way to drop in weight isn't to exercise (as such), and it isn't to eat less. All the logic that says those count, is valid, but you have to account for the body fighting back. The goal is to eat less because you don't feel hungry, not despite feeling hungry. Very few have the willpower to literally starve themselves.

You can definitely increase your burn rate by way more than 20% with heavy exercise. A Tour de France bicyclist will burn several thousand calories (4,000-7,000 depending on the stage and rider) in only about six hours. For comparison, a typical sedentary person will burn 2,000-2,500 calories per day. It can be physically difficult to eat enough at that rate, and riders lose a substantial amount of weight over the race. (A friend once told me about an endurance cyclist he knew who would eat a big bowl of cereal each morning, except instead of milk he'd use olive oil. Disgusting, but an effective way to get enough calories in.)

It's pretty tough for most of us to achieve anything like that much exercise, of course. Even Tour de France riders only do it for a few weeks at a time.