I like what LNR is trying to teach, even if it's not 100% the case all of the time. Many amateurs (myself included) swing first with their arm and the rest of the body often follows. LNR is trying to show that you don't have to always lead with your arms, you can lead with the uncoiling of your body and allow your arm to follow.
You're still using your arm, but it's following the motion of your body -- not the other way around.
He's exaggerating in order to illustrate the point. I'm sure if we watched him in match play, his right arm is not passive -- but he most likely is rotating his body with his arm following that rotation.