Stewart knows his audience. They're the sort of people who go looking for longer clips of stuff like that, so he's less concerned with accuracy and more so with comic effect.
Those 20 somethings (myself included) I mentioned readily criticize him whenever he misquotes or misrepresents. But it's still funny.
Stewart fabricates lies to denigrate political opponents for comedic effect.
One is honest,the othervis dishonest.