Dof you have a citation for that? I think it’s a myth. Letterman doesn’t even do the kind of jokes Carson did.
Check it out —
http://www.cbsnews.com/news/carson-feeds-jokes-to-letterman/
http://www.nytimes.com/2005/01/24/arts/television/24rcar.html?_r=0
http://usatoday30.usatoday.com/life/people/2005-02-01-letterman_x.htm
And from Letterman’s tribute to Carson after his death — the opening monologue was all jokes Carson had sent in the last couple of months. (As Letterman mentions in the second clip.)
https://www.youtube.com/watch?v=4BiHLK5lFvQ
https://www.youtube.com/watch?v=oDrxOM3jsxY