Where’s the line between covering a scoundrel as a news figure and giving him a promotional platform?

The question has consumed Megyn Kelly this week, after she showed a trailer Sunday night of her coming feature on NBC about Alex Jones, the conspiracy theorist who has questioned whether the Sandy Hook school massacre truly happened and asserted that Sept. 11 was an inside job.

“#ShameOnNBC” and “#ShameOnMegynKelly” campaigns broke out across Twitter, including from some Sandy Hook parents; JPMorgan Chase pulled its advertising, and Sandy Hook Promise, a group founded by a Sandy Hook parents to prevent gun-related deaths, canceled Ms. Kelly’s planned appearance at its annual gala this week.

Coming on only the third episode of her new NBC newsmagazine, “Sunday Night with Megyn Kelly,” the segment has become, as the technical television term goes, a hot mess.

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.

Their interviews were shown after Sandy Hook and, more to the point, after Mr. Jones began spinning his conspiratorial yarn about the mass shooting (ABC says the interview video in the “Nightline’’ segment came from 2010).

“They didn’t get into the conspiracy,” Ms. Kelly said, referring to those CNN and “Nightline” appearances and Sandy Hook. “I press him.”

Mr. Jones was also scheduled to appear on “The View” next week, though a spokeswoman for the show told me that he canceled the interview (she declined to speculate on whether “The View” would have canceled the appearance after the blowback for Ms. Kelly and NBC).

The test for Ms. Kelly, of course, will come in that interview, how it’s packaged on Sunday night and how aggressively she questions him.

The argument from several of the Newtown parents is that Ms. Kelly shouldn’t be interviewing him at all.

“I hear what Megyn is saying about journalistic integrity — you have to expose the unsavory parts as well so that people understand them,” said Nicole Hockley, a founder of Sandy Hook Promise, whose son Dylan, 6, was killed in the massacre. But, she said, “It gives him a national platform — a much bigger platform than he’s had in the media before — which serves to recruit new supporters to his cause and tell people that there are conspiracy theories out there they might not be aware of.”

In the end, she said, “People like me are going to have to deal with the fallout.”

Ms. Hockley said that Mr. Jones’s promotion of the fiction that Sandy Hook was a hoax has led to harassment campaigns and even death threats against her and others who lost children and loved ones in the massacre, which is just sickening. So you can see the concern. Mr. Jones’s conspiracy theories can have truly dreadful, real-life consequences.

Part of the problem for Ms. Kelly came with the release of the trailer for her interview this Sunday, which included snippets in which he waxed conspiratorial about how “9/11 was an inside job” and played down his previous assertions that Sandy Hook was a hoax. Ms. Kelly tells Mr. Jones, “that doesn’t excuse what you did and said about Newtown, you know it,” but she is also shown laughing lightly as he says, “we didn’t get to any of the really important stuff” (about supposed animal-human hybrids).

Then there was a photo Mr. Jones released of him and Ms. Kelly side by side in his car. It has a look and feel of a selfie — though NBC says it wasn’t a selfie — giving the impression of a chummy get-together, which critics have seized upon.

It’s not the first time that has happened, albeit without the same drama. In the “Nightline” segment, the correspondent, Dan Harris, calls Mr. Jones a “premiere purveyor of what could be called paranoia,” but he is also shown tossing a football with Mr. Jones, even saying, “When you turn the cameras off, Jones is a pretty calm, friendly guy.”

But those were different times, before the election of Mr. Trump and before the nation’s divisions boiled over to the point that even corporate advertisers are being pressed to take sides.

“Too many people expect their media to choose sides,” Ms. Kelly said. “They want ‘evisceration journalism,’ and I think there are a lot of people who are very angry that Donald Trump is president and a lot of people who believe Alex Jones played a large role in it,” which, she said, she wouldn’t disagree with.

The broader goal of Ms. Kelly’s segment on Mr. Jones, she said, was to explore, “his influence and his — for lack of a better term — method for putting information together to figure out how he got to be so important in the president’s world, in millions of people’s world”

Ms. Kelly said her demeanor with Mr. Jones — including the photo in the car — was in part to get him to talk, while still challenging him. “I don’t know if people know how journalism works, but you don’t show up, scowl at the subject of your interview all day, cross your arms and try to project as frosty an image as you can,” she said.

So, where do I come down?

You can’t argue with the journalistic imperative; that’s why I interviewed Mr. Jones myself. As Ms. Kelly told me, while people may wish Mr. Jones didn’t exist, “he does exist and his influence is growing exponentially.”

At the same time, you can’t argue with the pain of the families of Newtown. The continuing, outrageous questions about the biggest tragedy that could befall any of us only worsens and prolongs the suffering.

And talking to a conspiracy theorist like Mr. Jones is not like a typical interview. Facts and reason have to square off against the fanciful and the fallacious. Absurd arguments are hard to combat because the person making them is not playing by logic’s classic set of rules.

All of which is to say, if the interview is done, it must be done carefully, with the best journalism that can be brought to bear. If the trailer NBC presented teasing the piece showed had shown that was the case here, which it didn’t, there might not be so much outrage.

Ms. Kelly said, “I do not think people will emerge from having seen this piece thinking anything other than 26 people were brutally murdered in Newtown, Conn., and there is a group of people that refuses to acknowledge that.”

The proof will come when NBC shows the piece on Sunday night, when the segment can be judged in its entirety.