Well, sigung keeps most of those things to himself. From what I understand, traditionally when masters challenged each other to trade hands they did so with little fanfare, in a neutral place, and did not talk about the results afterward. (My source on this is from an article about Jack Man Wong's challenge match with Bruce Lee, it's on the Internet somewhere, if I can find a link I'll post it.)
The only challenge match I can tell you about is a well-known (among WL students) story. In the 1970s a TKD stylist walked into MC's original school (across the street from my office BTW) and challenged him to a match. MC said, "OK, but only if you follow me onto the street." The challenger agreed, only to watch as MC jumped out the open 2nd-story window onto the sidewalk. MC then turned and beckoned the challenger to come down. The TKD stylist immediately withdrew his challenge and left -- by the stairs.
A 2nd-story window isn't much by Oom Yung Doe standards, but MC did have to gauge the outward distance of the jump since the steel support beams of the green line el are less than a sidewalk's width from that window.
There is a great streak of violence in every human being. If it is not channeled and understood, it will break out in war or in madness. ~Sam Peckinpah