Burning more calories than you take in, and taking in fewer calories than your body needs are equivalent statements. But the harder you work your body, the more damage you create that needs to be healed. If you do a lot of work and cut calories to generate fat loss, you are at risk of messing yourself up.
You have to do enough weight training to keep up your lean tissue, but you need less than you expect to maintain. Martin Berkhan's clients do 2x-3x/week and gain lean mass while losing fat. I've been working out every 3 days and improving body comp more than the modest weight loss (1 lb/week) could explain.