In case you missed it, Rather said the CBS Evening News is in a tailspin because CBS tried "to bring the 'Today' show ethos to the 'Evening News,' and to dumb it down, tart it up in hopes of attracting a younger audience." It is understandable why Moonves dismissed these remarks as sexist, and it's also understandable why Rather wants to believe that things would have been different if he hadn't blown himself up in the Bush-National Guard forgery fracas. But the argument is a sideshow.
Moonves is right that unless CBS can find ways to skew the Evening News audience under 60 years old, the show is toast. He's wrong, however, when he implies that the choice of the right anchor, or style, will accomplish this.
The evening news shows are dying for the same reason the newspapers are dying: the next generation of viewers/readers are getting their news online (or from Jon Stewart). Because the online medium is simply a better medium for delivering news, nothing the TV networks do will change this trend.