I heard on a podcast that pounds of fat burn calories at a different rate than pounds of muscle. The thinking is that a pound of fat, sitting idly over the course of the day, requires X calories, whereas a pound of muscle, sitting idly over the course of the day (that is to say, without being vigorously exercised) requires X+Y calories, because muscle is "more expensive" for your body to maintain, nutritionally speaking. That would seem to imply that if one were to undertake a workout regimen designed to build muscles (lots of strength training, minimal focus on cardiovascular activities) that the additional muscle mass would result in the body burning more calories per day while it was in its "at rest" state. That would seem to imply that one would then be able to lose some of their fat weight, as they would now have a more favorable ratio of caloric intake to caloric expenditure.
Is this a healthful approach to weight loss? If someone were in a situation where they were overweight (but not yet obese) is strength-training a logical approach to achieving a higher fitness level?