Ms. Kelly was respectfully unapologetic when I caught up with her late Tuesday.

“What we do as journalists is we shine a light on those with power, those with influence, those who have become culturally relevant,” she said. “Of course, it’s upsetting to know that doing that causes any upset to the Newtown families, many of whom I know well. But I have to do my job.”

Mr. Jones, she noted, has found new prominence in the Trump era. He’s gaining in popularity and, perhaps more important, has back-channel communications with the president of the United States, who has been known to espouse some of his theories.

“As journalists, we don’t get to interview only the good guys — that’s not journalism,” Ms. Kelly said. “It’s going to be very difficult for us to keep an eye on the more controversial figures of our time if we never talk to them.”

I talked to Mr. Jones myself for a column in February. He informed me that he was hoping for a White House press credential for his organization, Infowars, and that he had spoken with Mr. Trump by phone on more than one occasion and even offered the president advice, though he said Mr. Trump didn’t need it. As such, I wrote, Mr. Jones was “newsworthy for taking on a new role as occasional information source and validator for the president of the United States.”

I didn’t receive the same amount of grief Ms. Kelly has, which she pointed out to me. While television is a different ballgame — giving interview subjects more room to have their say in front of more people than the average news site — Ms. Kelly noted the reaction was similarly low-key for Piers Morgan of CNN and “Nightline” on ABC when they featured interviews and segments on Mr. Jones in early 2013; there were no advertiser pullouts or major Twitter campaigns against them.