All BS.
Rev-matching SAVES the synchros. And rev-matching is NOT shifting without the clutch.
Granted, it's not needed as much with synchronized trannies, but it will still save the synchros in the long haul.
It's also referred to as "Heel and Toe" shifting. Basically, the left half of your right foot is on the brake, and between shifts, you shift to neutral, let the clutch up, and blip the throttle with the right half of your right foot. Then shift to your gear. Some folks do it with the ball of the foot on the brake, and blip the throttle with their heel. It works best on a car where the brake pedal and gas pedal are about the same height.
It is still a valuable technique for driving an MTX SHO on the track where you may be downshifting from 3rd or 4th to 1st or 2nd for a corner. On an older tranny, it won't always want to go into gear with worn synchros. I never practiced it enough to get good at it, but i have just done the technique to rev-match in neutral on certain tracks where I would downshift.