The group that represents reporters and news organizations that cover the White House pushed back against attacks on the media Saturday night at its annual dinner to raise money for journalism scholarships and celebrate the First Amendment.
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Bernstein also recalled their time reporting on the Nixon administration, citing some of Woodward's advice about reporting.
"Almost inevitably, unreasonable government secrecy is the enemy," Bernstein said. "And when lying is combined with secrecy, it's usually a road map to what the real story might be."
President Donald Trump has levied attacks against news organizations that covered his campaign and now his presidency, calling stories "fake news" and calling the media the "enemy of the American people."
"We are not fake news. We are not failing news organizations. And we are not the enemy of the American people," said White House Correspondents' Association President Jeff Mason.
The president said he would not attend the dinner this year and White House staffers said they will also skip the event "in solidarity" with the president. Trump held a rally in Harrisburg, Pennsylvania on Saturday night.
But Trump did attend the Correspondents' Dinner as a guest in 2011, when he was teased by President Barack Obama and comedian Seth Meyers over Trump's support for the "birther movement," which questioned whether Obama was an American citizen.
The annual dinner is held by the WHCA to celebrate the First Amendment and raise money for journalism scholarships.