Allright, my understanding of the situation:
The torque generated by the thrust difference has to be counteracted somehow with opposing torque. I can only think of one way to generate this opposing torque: The fin. We either change the camber of the fin (rudder) or the angle of attack of the fin (slip).
In either case, the force to the side of the dead engine has to be counteracted by another lateral force. Wings level, this will mean a slip into the dead engine. Rolling slightly into the live engine will give you the same effect without trying to shove the aircraft sideways through the air.
When we run into the end of the authority of the rudder as far as counter-torque generation goes, the only possibility to further decrease the speed or increase the power on the remaining engine will be to slip more towards the good engine, in order to increase the slip and thus the angle of attack of the fin.
How about it?
Regards,
Fred