The human body is absurdly efficient. Fat weight is tackled by reducing calorie intake (using whatever tactic works for you). Exercise only makes a small difference by comparison.
Edit: for example, you could jog for almost an hour to burn approx 460 calories. Or you could just not eat 1 cinnamon swirl krispy kreme. Ate two at the family BBQ? You just gave your body enough fuel to light jog for 2 hours. A large vanilla milkshake has enough fuel to keep you jogging for an hour and a half. Stop overeating first or gym weightloss is useless.
Exercise can burn a ton of calories, but in order to be able to do that level of exercise you have to be reasonably fit. For someone who doesn't have a ton of stamina, I agree that diet is much more effective.
Exercise in someone not particularly fit is also likely to trigger a stress response and their appetite will overcompensate. Exercise is good - everyone should be doing it - but for fat loss is pointless unless eating is well under control.