All "unauthorized" clips of Letterman's 10 minute apologia have now been removed from You Tube, and (contrary to common practice) CBS never posted a similar "authorized" clip on either You Tube or on CBS.com, all reportedly at the request of Mr. Letterman's production company, Worldwide Pants.
That all makes for an interesting decision tree. Have a string of affairs with employees over many years. Then, when confronted by an extortionist, take the "high road" and admit the affairs on your highly rated show. But do so without any advance publicity and in a rambling way that makes it unclear for several minutes whether it is a heartfelt confession or just another "bit" played for laughs. And then immediately after the fact take all possible action behind the scenes to prevent that clip from being seen again.