Sure, I know it's not obvious to most who might never have considered it, but the author is someone who's been deep in the fitness world for over 20 years by his own bio.
Other things that are not as commonly understood: Not all exercise builds muscle, and building muscle is far slower than most people estimate. You don't simply start doing the elliptical 30min a day and gain any amount of measurable muscle in 2 months. You have to lift progressively heavier things to do that, and even then it's 2lbs a month for men to start, and half that for women. (and that's for younger people than most here)
And doing cardio for long periods (slogging out a 10 mile run, etc.,) your body isn't always as calorie efficient on the burn on mile 6 as it was on mile 1.
But yes, having a fit strong body that can move and lift and go is one that is more efficient and a better metabolizer of what you do eat. So it does all work together, especially over the long haul. That's why the goal for most people shouldn't be simply to "weigh less" but to reduce body fat, increase cardiovascular capacity, strength, flexibility, fitness.