Top trainers will all concede that NUTRITION is king. There are a few reasons:
1. It's not that hard to create a calorie deficit simply by removing the wrong-food culprits. If you were to eat nothing but clean, balanced food and eliminate junk food, you'd most likely create a calorie deficit meaning, when you would burn more calories than you consume which would cause you to lose weight, even with no exercise at all. Your body needs calories just to function so it will use up these clean, body sustaining calories leaving no excess, ie nothing to store as fat.
2. You CAN outeat exercise, pretty easily if you're not careful. People have a tendency to think they can eat more because they worked out which can be true ONLY if if's clean food. An extra piece of grilled chicken and some veggies - great! A stop at McDonalds - chances are you'll undo the the calories you just worked off, not to mention the unhealth and what those calories do to erode your body.
Yes, exercise can absolutely speed up weight loss (not to mention getting you fit and strong) but only if you're also eating nutrient-rich meals with little to no junk. FOOD is your best tool for reshaping your body.
Food is your clay, your workouts are the chisel.