That seems to be the question... and the answer is no, you do not need to screw the bar into the wall / door frame. The bar, with it's hard rubber ends, telescopically expands to snugly and safely fit into place. The included screws and cups are for additional security, but from other reviews I've read seems to be splintering the door frame.
I have secured my bar in my hallway (serves also as shirt hanging space) where there is a solid wall either side - the only place in my flat where there are opposite solid walls, so I discovered. A friend secured his on his roof between two chimney stacks which looks rather ace... as do our new shoulders.