Can watch this on demand, and what a great opportunity: http://www.americanthemovie.com/?page_id=1267

I will confess, I mix up Hicks and Will Durst (they got lumped together in a "I heart this guy" drawer in my messy memory filing system late 90s), so I went poking around to see which one this was, confirmed it was not the guy who did the great Livelyhood series, that was Durst, and found this, Letterman apologizing to Hick's mom for cutting Hick's act years earlier, and Letterman than played the entire sketch.

http://videogum.com/49601/david_letterman_finally_airs_b/tv/late-night/