If this was the case then why not use polarized magnetized screws in the core, or apply magnets to where the poles are located on the can to increase permeability and attraction.
yes the screws are magnetizable but are not in the winding in a sense where the right hand rule applies to the direct of the current, where as the winding is not directly influenced by a non connected inducted pathway. So the screw basically acts a device that is attracted and opposed to a magnet.