When The Daily Show first started on Comedy Central they poked fun at both the right and the left. Once the show started can popularity all of the sudden they just attacked conservatives and the show fell apart (for me anyway, for brain dead liberals it only gained in popularity).
I watched when John Kerry ran for president. Kerry is comedy gold. You wouldn't even have to try very hard make jokes about him because he is a walking joke. But I never once saw John Stewart ever say anything slightly negative about Kerry, in fact most of the time he never talked about him.
I watched as Stewart just danced completely around the actual facts just to make up some lame set up for his lame take down, none of which was based on any kind of reality. That's when I had enough. The show I used to think was really funny became a joke machine for the mentally retarded.
I would say that is why Stewart left the show but I watched part of his show on Apple TV and he is even worse over there. I don't know if Apple has tight reigns on Stewart or not. I would think he would have carte blanche. The sad thing is that Stewart is a smart guy and he is truly funny when he wants to be. But now he is just a shell of his former self because he won't make jokes based on actual facts.
It is like you said, there has to be an element of truth in it in order for it to be funny. Fabricating a set up based on a lie and then creating a take down off of that set up is just not funny.