Yeah, the Daily Show members explicitly reject responsibility. They're comedians. It's not their driving goal to provide high-quality information every night. Jon Stewart claims that a low point of the job is the fact that they have to make jokes about something which is ultimately not funny.
On "Sit Down Comedy with David Steinberg," Steinberg and Jon Stewart discussed how Nixon strongly intimidated Steinberg over some silly joke, and Stewart pointed out that he's not nearly as threatened:
Stewart: If whatever powers that be felt that the effect we were
having was impactful, there is no question that there would be
repercussions.
[...]
Stewart: But the interesting thing about the show is, again it's
the point about not falling in love with your audience. Because I
do think at times people who watch this show get the idea that we
are warriors in their fight. In their activism.
Q: And what's the matter wtih that?
Stewart: We're not. And never will be. And the difficulty is that
you'll never be them. And so ultimately, they will always be
disappointed by you. Because you will say things that are
upsetting to people who believed that you were leading them into
battle. And you know, that's the danger of it. But that's why you
don't fall in love with the audience, and you only... you trust
your instinct with the people around you.
Tayssir