OK thanks, Dan. I think the term "Output" coordinate system was initially confusing me because there is no output layer for this tool. However, what I think they mean, and what you might be saying, is that this could really be considered the "Analysis" coordinate system.
So, is the Default be the Input Layer coordinate system?
Then (and maybe what you're describing below), for display alignment purposes, the data will still project on-the-fly to the Map coordinate system, regardless?