If True, Not Funny

A friend of his reported:

Edward Klein, speaking to WAMU guest host Katty Kay, said one of Kennedy's "favorite topics of humor was, indeed, Chappaquiddick."

"He would ask people, 'Have you heard any new jokes about Chappaquiddick?'" said Klein, a former Newsweek foreign editor and former editor in chief of the New York Times Magazine.

They say it's good to laugh at your failings, but...
is that really true no matter what?