From the moderator's chair on a debate night 10 years ago, Dominic Carter asked then-Sen. Hillary Clinton the big question on New Yorkers' minds: Was she mulling a presidential run in 2008 that would pull her away from her constituents?

Clinton, running for reelection to the Senate against Republican John Spencer, offered an indirect response. Carter followed up but still didn't get a straight answer. He moved on, anyway. Looking back, the former NY1 anchor says he didn't press harder partly because Clinton is a woman.

"To be honest with you, and to put political correctness aside, perhaps if she was a man I would have pushed a little more," said Carter, now a political commentator at Verizon Fios News and RNN in New York. "We were very conscious, me and my producers, that with the first woman candidate with a real shot of going to the White House, we didn't want to have a Lazio moment."

By "Lazio moment," Carter meant a sexist one. Rick Lazio was Clinton's Republican opponent in the 2000 Senate race. When he walked over to Clinton's lectern during a debate that year — pointing angrily as he railed against outside spending — Lazio was widely criticized, including by New York Times columnist Maureen Dowd, who slammed him for "trying to cow a female opponent with ... muscular histrionics."

Today, the fear of an accusation like that still hangs over moderators, as well as Clinton's male rivals in politics, according to Carter. He said he is sure that Donald Trump's campaign manager, Kellyanne Conway, has played video of the Lazio episode for the Republican presidential nominee, and he is equally confident that this year's male moderators — Lester Holt, Anderson Cooper (paired with Martha Raddatz) and Chris Wallace — will take care not to appear overbearing.

"Anybody that tells you they're not walking a fine line, in terms of gender, is lying to you," Carter said.

Carter knows, of course, that his comments could be used to advance a favorite Trump narrative — that Clinton gets off easily because she is a woman.

"Frankly, if Hillary Clinton were a man, I don't think she'd get 5 percent of the vote," Trump said in April. "The only thing she's got going is the women's card."

Carter insists he's not talking about going easy on Clinton or being more aggressive when questioning Trump.

"You have to be fair to everyone," he said. "You cannot give Hillary Clinton an advantage because you're afraid of being called sexist. So here's how you do it: You try as much as humanly possible to make sure that they receive the same time. And you try to remove yourself. Let those two go at it. If I can remove myself, where I'm not the major factor in the debate, and it's between Hillary Clinton and her opponent, then I have succeeded. If you wake up the next day, and your name is part of the headline, in my opinion, you've failed as a moderator."

Carter's advice to get out of the way is consistent with what Wallace and previous presidential debate moderators Bob Schieffer and Jim Lehrer have said about live fact-checking — basically that moderators shouldn't do much of it.

"I do not believe that it's my job to be a truth squad," Wallace said on Fox News this month. "It's up to the other person to catch them."

As Carter sees it, the presence of Clinton adds one more reason for moderators to act as mere facilitators, aware that badgering a presidential candidate always looks bad — and, in this case, could potentially cross a line into sexist territory.

"No journalist — I don't care what they say to you — no journalist wants the headline to read that they were sexist against a person who may go down in history," Carter said. "You want to try to be fair to everybody."