I'm pretty sure we know this isn't true at all. Diet is the greatest contributing factor to weight gain or loss. Exercise will make you healthier. In your example, cardio (e.g. high-intensity interval training), will give you a stronger cardiovascular system, which will likely make you "feel better" (less strained, more comfortable) when moving around in the world. And strength training (e.g. resistance training) will make you stronger and more comfortable when trying to lift things or even yourself.
Exercise is for health/muscles/good muscle shape etc... Sport will actually make you want to eat more. For weight loss (if there aren't health conditions/hormones that mess things up) it's just diet(what you eat and how you eat and how much you eat)
The big problem with sports and serious exercise is that this desire to eat more tapers off very slowly if you start exercising less. I know several people from college who where pretty serious athletes while at school, but then started exercising much less after graduation, and they all put on a lot of weight very quickly, even though they stayed reasonably physically active and are on the whole pretty fit.
cardio is important, but you can easily eat more calories than you burn in an average run. a small side of fries with your burger would undo the caloric burn.
"shoulders are built at the gym; abs are built at the dinner table"
