Joaquin Phoenix's appearance was eventually revealed to have been part of his "character" for the film.
Jay mentions Joaquin Phoenix's appearance on the show
Still photo from Joaquin Phoenix's famous visit is shown when Dave says he once talked to an alien.
Joaquin's interview with Letterman is shown
Excerpt shown of Joaquin's previous infamous visit - Joaquin, still on camera, removes his sunglasses after the interview is over, and shake's Dave's hand, hinting that the interview was indeed staged.