Yes, calories burned during exercise is no a major part of weight loss. However with the right training you can raise your base metabolism. Otherwise when you diet your metabolism tends to slow, which offsets your decreased eating.
this is not untrue, but a severely over-exaggerated cliche. whatever amount you can raise your BMR via exercise, is not going to be significant enough to make any kind of difference. not to mention, if we are going the stereotypical way of copious amounts of cardio, even worse because it does even less for your BMR.
I remember reading that the difference between the fastest and slowest metabolisms worked out to somewhere around 1-200 calories per day. Not a huge difference.