I'm assuming you got rule quote from wikipedia, because that's the only place I can find it.
^ NFL Rule 3, Section 21, Article 2, Note 2: "When a Team A player is holding the ball to pass it forward, any intentional forward movement of his arm starts a forward pass, even if the player loses possession of the ball as he is attempting to tuck it back toward his body. Also, if the player has tucked the ball into his body and then loses possession, it is a fumble."
That also says nothing about it having to be a QB. So any player can do a forward motion with the ball anywhere on the field and the penalty applies. Hell, it doesn't even say it has to be an offensive player. I've never seen the official NFL rulebook and I'm pretty sure that this quote didn't come from it. I could be wrong though...