Time was, when a guy was caught with his zipper down, he would fight to keep the news private. Nowadays, and rightly so, he admits to whatever the affair so as to avoid being extorted for large sums of cash. It might embarrassing, but at least he is not beholden to someone trying to steal from him.
Remind me to tell you about the time I... No. Not yet. Not for quite a while yet.
Anyway, here's Letterman's admission from the October 1st show: