Definitely a myth. I've been at the same weight I am now more than once in my life. However, in the past I was never lifting, now I am. I have a number of pictures (and clothes) from both of these times and there's a HUGE difference. I'm much smaller now and am wearing at least a size smaller too.
Like
nelie said, after an intense lifting workout your muscles retain a lot of water so the scale normally goes up and your biceps might look HUGE but it's only temporary. I've had friends who have made the "bulking-up" claim too but they were always very overweight so they had a lot of fat covering those muscles too.
Oh, and besides looking smaller at the same weight you actually burn MORE calories throughout the day than an equivalent cardio workout. Oh, AND you're stronger and have more energy.
The only thing that is very important to remember: EAT LOTS OF PROTEIN, if you are heavy lifting you need that protein to fill you up so you don't end up going overboard with other types of calories.
ETA: Another great advantage to lifting? Broader shoulders! It slims down the rest of your body and gives a great focal point when you're dressing yourself!