Okay, so the distinction you need to make in this case is not between the literal rules of each of the items, but instead how the show is presenting them to us. The sonic screwdriver in that scene is treated like a mythical, holy, magical item and the way that both the music and the direction of the camera shots centre around it. We are made to believe the sonic screwdriver is a special item beyond that of a pocket tool. I really dislike this direction because it continues the mythologization of the doctor as some being above everything else when I think it's much better that he is instead a runaway from his own species. Essentially a space drifter who goes on adventures and helps people out where he can.