Hostra University students playing the roles of the candidates and moderator go through a rehearsal for the first presidential debate in Hempstead, N.Y., on Sunday. (Rick Wilking/Reuters)

On the eve of the first presidential debate of the 2016 election, Donald Trump’s campaign manager, Kellyanne Conway, said on Sunday that she doesn’t believe moderators should fact-check the candidates. And the head of the commission that puts on the debates agrees.

“I don’t think it’s a good idea to get the moderator into essentially serving as the Encyclopedia Britannica,” Janet Brown, executive director of the Commission on Presidential Debates, said in an interview with CNN’s “Reliable Sources” from Hofstra University, where Monday’s debate, moderated by NBC’s Lester Holt, will be held. “I think it’s better for that person to facilitate and to depend on the candidates to basically correct each other as they see fit.”

Hillary Clinton’s campaign thinks that’s unfair, given the Republican nominee’s frequent aversion to veracity.

“All that we’re asking is that if Donald Trump lies, that it’s pointed out,” Clinton campaign manager Robby Mook said on ABC’s “This Week with George Stephanopoulos” on Sunday. “It’s unfair to ask that Hillary Clinton both play traffic cop with Trump — make sure that his lies are corrected — and also to present her vision for what she wants to do for the American people.”

Conway said Team Clinton is running scared.

Slideshow: Preparations for the presidential debate at Hofstra University >>>

“I really don’t appreciate campaigns thinking it is the job of the media to go and be these virtual fact-checkers and that these debate moderators should somehow do their bidding,” Conway told Stephanopoulos. “I can understand why the Clinton camp is very nervous, because Donald Trump has got great present stature. He’s a brilliant debater.”

“He’s like the Babe Ruth of debating,” Conway added. “He really shows up and swings and does a great job.”

Both Trump and Clinton agreed to the moderators and formats announced earlier this month by the bipartisan commission. Holt will moderate the first debate from the Hofstra campus in Hempstead, N.Y., on Monday. CNN’s Anderson Cooper and ABC’s Martha Raddatz will co-moderate the second debate, a town-hall style forum, in St. Louis on Oct. 9. Fox News’ Chris Wallace will moderate the third and final presidential debate in Las Vegas on Oct. 19.

Story continues

Wallace said that “it’s not my job to be a truth squad.”

“The commission asks independent, smart journalists to be the moderators, and we let them decide how they’re going to do this,” Brown said. “But I have to say, in our history, the moderators have found it appropriate to allow the candidates to be the ones that talk about the accuracy or the fairness of what the other candidate or candidates might have said.”

She added: “I think, personally, if you are starting to get into the fact-check, I’m not sure what is the big fact and what is a little fact?”

Related: Clinton campaign: Debate moderators should fact-check Trump

The role of moderator as fact-checker became an issue at NBC’s Commander in Chief Forum earlier this month when host Matt Lauer failed to challenge Trump’s false assertion that he “was totally against the war in Iraq,” despite the fact that Trump told Howard Stern the opposite in 2002.

Trump later said the harsh criticism of Lauer’s performance was proof that the upcoming debates would be “rigged” against him.

“Everyone’s saying that [Lauer] was soft on Trump,” he said on CNBC. “Well, now the new person’s going to try to be really hard on Trump just to show, you know, the establishment what [they] can do. So I think it’s very unfair what they’re doing.”

What would be fair, then?

“I think we should have a debate with no moderators,” Trump said. “Just Hillary and I sitting there talking.”

Last week, Trump predicted that the moderators of the first two debates are prejudiced against him.

“By the way, Lester is a Democrat,” Trump told Fox News’ Bill O’Reilly on Monday. “They’re all Democrats.”

Fact check: That is not true, at least in Holt’s case. As Time magazine noted, the “NBC Nightly News” host has been registered as a Republican since 2003.