The amount of calories burnt through exercise is completely negligible. For instance running a mile at a good pace will generally burn around 100 calories, the same as you get from eating about one banana, or about drinking about half a bottle of Coke.

Exercise does have many positive metabolic and other benefits, but not anywhere enough to be a causal explanation on its own. If people started walking 5 miles a day, every day, not only would there still almost certainly be a widespread and growing obesity epidemic, but there's even an argument that it could be worse. Increases in activity tend to drive increases in hunger which will typically surpass caloric deficits if somebody is not actively controlling their diet, in which case they would not be fat in the first place.

This is made even worse by misleading advertising which will do things like showing fit athletes drinking Gatorade, Coke, etc during their training or competition. And somebody goes and does a couple of miles on a training bike and does the same thing - which is going to send their net caloric input skyrocketing.