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With a real news anchor sidelined and a fake news anchor stepping down, it seems far-fetched to say that Jon Stewart has had more impact on the news business than Brian Williams.

But it’s true.

All the praise for Stewart since he announced he’s leaving the “Daily Show” later this year has focused on the late-night franchise he created. And he has clearly turned himself into a premier social, political and media critic, all the while insisting he is just a mere comedian. And I say that as someone who’s interviewed Stewart many times, been on his show and been the target of his barbs.

Stewart is voluntarily leaving the Comedy Central stage to a standing ovation. And what’s largely been overlooked is how the bogus anchor influenced real anchors. I first noticed this in 2004, when Stewart played a clip of President Bush introducing nominee Michael Hayden: “He’s the right man to lead the CIA in this critical moment in our nation’s history.” Then he played a bite of Bush introducing Hayden’s predecessor, Porter Goss: “He’s the right man to lead this important agency at this critical moment in our nation’s history.”

The same clips soon appeared on “NBC Nightly News,” with credit to Jon Stewart.

Soon other network and cable shows started borrowing Stewart’s technique of using videotape to spotlight inconsistencies and absurdities in the pronouncement of public figures.

That is what viewers, particularly younger viewers, love about Stewart, the sense that he cuts through the pomposity of politicians and pundits and gives it to you straight.

Stephen Colbert, Stewart’s protégé, once told me that journalists would privately tell him, “I wish I could say what you say.” And he would think, why couldn’t they say what he said, in their own way, and blow the whistle on political hypocrisy?

Now Stewart makes no secret of being a liberal and has obviously been much harder on Republicans. But when he criticizes President Obama, it stings. When Kathleen Sebelius botched an interview with Stewart on ObamaCare, it probably hastened her departure.

Stewart’s great dodge, which he’s expressed to me and many others, is the just-a-comic line. But that undercuts the importance of what he does. Sure, he selectively and sometimes misleadingly edits the clips, but he’s trying to get at a core argument — one that you may agree or disagree with, but which breaks through the usual blather.

One dirty little secret is that pundits — and politicians — love to be mocked by Stewart. Merely being on the “Daily Show” or “Colbert Report” was a sign of having made it, like having someone play you on “SNL.” And then you could fire back and whip up a little exaggerated feud. (Guilty.)

A few years ago, Stewart landed high on a most trusted newsman list. Which is a little silly — he’s not a newsman — but he does traffic in real news. And at the moment, he’s a heckuva lot more trusted than many real journalists.

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