Lorie, it's another fitness myth that just won't die. At least it's based on some truth, compared to some of the other nutty myths that persist. Muscle does in fact use a few more calories than fat, but, unfortunately, not enough to make a difference to any of us.
Sleeping longer can probably do more for weight loss than strength training. One study showed that people who slept four hours or less per night were 73 percent more likely to be obese than those who slept between seven and nine hours a night. Those who got five hours sleep a night were still 50 percent more likely to be obese. This may have to do with the amount of leptin produced in the brain, which is a natural appetite suppressant, but I don't think this has been conclusively determined.
Nonetheless, strength training is VERY important for a whole host of reasons. My primary reason is to avoid the frailty of old age I see in so many of my clients, and to prevent osteoporosis.