Near the end of Monday’s presidential debate between Donald Trump and Hillary Clinton, Trump stood by his oft-contested claim that he opposed invading Iraq in 2003, despite a tape-recorded interview with Howard Stern in 2002 to the contrary. This time, however, he suggested a new source to back up his assertion. “I had numerous conversations with Sean Hannity at Fox,” he told the audience. “He and I used to have arguments about the war. I said it’s a terrible, stupid thing; it’s going to destabilize the Middle East. And that’s exactly what it’s done.” He added: “Nobody wants to call him. Nobody calls Sean Hannity.”

As it happens, I met with Hannity the week before in the office of his radio studio in Midtown Manhattan in the course of reporting a coming article. Hannity told me then what he reiterated in an interview with Trump immediately following the debate — that such conversations did, in fact, occur. “He would watch the TV show and call me, and he and I would go at it over the Iraq war,” Hannity said. “I remember these conversations vividly. I remember saying to him, ‘I agree with you, take the oil! But this is why we need to go into Iraq.’ ”

Given that Hannity was and is a fierce advocate of the Iraq war, and that Trump had no particular political or foreign-policy expertise, I asked him: “Didn’t you ever think to yourself, Why am I spending all this air time having conversations about Iraq with this guy?”

“No, because we kind of hit it off from the beginning,” replied Hannity, who had known Trump for about a decade before the Iraq invasion occurred. He added: “He’s kind of the opposite of a politician who spends a lot of time hiding their flaws. He’s just the opposite. What you see is what you get, and there’s nothing beneath that.”