What I am calling a flared fitting is the trumpet looking copper thing that was soldered to the 1-inch copper pipe. The black plastic nut you reference is then screwed over the copper "flared" fitting. Maybe I could just line up the new softener and use the existing plastic nut to screw onto the new softener (?). I think the Culligan uses some type of flared plastic fitting in order for the copper flared thing to seat properly. The Culligan has no copper attached to it, only plastic.