So getting back to the original question, the Duplicate Rule does not allow me to control a duplicate or to cause duplicates to fight each other. If I control King Saul in battle and my opponent controls King Saul in a side battle, that does not seem to violate either portion of the Duplicate Rule.
If we do want to go with "Field of Battle," the REG or rulebook would have to add that distinction since it is not addressed currently.