No one at Harley ever proclaimed that their stability control can not handle towing. It's this statement that makes the difference.
This situation is not unusual at all even in vehicles which are designed for towing. I have a Ford Econoline full size conversion van which I use for towing my trailers at times. These are available from the factory with hitches yet Ford still recommends I disable part of the stability control system when towing and also disable overdrive unless I am on the highway.