When I go hiking for a couple of weeks (with significant elevation gain each day), I eat like a pig. I mean, something like 5000 calories a day. I lose weight over that time. So it's possible to lose weight through exercise, however you really do have to spend a very significant chunk of each day doing it for it to work.
Not eating as much takes much less of your busy day.
Not eating as much takes much less of your busy day.