There’s an important, often overlooked bit of context to President Trump’s interview with “60 Minutes” that aired Sunday night.

His interviewer was Lesley Stahl, a veteran of such exchanges who had first interviewed Trump (and his family) soon after he won election. Earlier this year, Stahl revealed a conversation she’d had with the then-candidate shortly before the interview in which he told her that he constantly railed against the “fake news” “to discredit you all and demean you all, so when you write negative stories about me, no one will believe you.”

Stahl, then, was prepared to allow someone else to undercut Trump's untrue statements: Trump himself.

It has been a while since Trump’s rhetoric has been challenged in any significant way in a television interview. On most of the occasions in which he has granted interviews lately, they’ve been over the phone or with sympathetic (if not openly supportive) interviewers from Fox News Channel. The sit-down with Stahl was neither of those things, both of which muffle, in some way, the ability to hold Trump accountable for saying false things.

Consider this exchange between Stahl and Trump on North Korea.

STAHL: What about North Korea? Talking about accom—

TRUMP: Well, I consider it a, so far, great achievement. Look, we —

LESLEY STAHL: You say “so far”?

TRUMP: It’s always so far, till everything’s done. I — I — you know, deals are deals, okay? Whether it’s a real estate deal or a retail deal, it doesn’t matter. But I will say this. The day before I came in, we were going to war with North Korea. I sat with President Obama —

STAHL: We were going to war?

TRUMP: — and — we were going to — I think it was going to end up in war. And my impression is — and even in my first few months, I mean, that rhetoric was as tough as it could possibly get. Doesn’t get any tougher than that. Nobody’s ever heard rhetoric that tough.

Now compare that with what Trump said in an interview conducted late last week with Time magazine from Air Force One by phone.

“Look what I’ve done with North Korea,” he said. “When I came in, the day before I came in, if you look, we were going to war with North Korea. President Obama said it was by far his biggest problem. Of course he gave me a lot of problems with a lot of things, including Iran. Look at Iran.”

That “war” claim is important: Trump is hyping the importance of his efforts with North Korea by claiming that he averted a very serious alternative. But as Stahl interjects, that’s not true — and Trump backs off his claim: “I think it was going to end up in war.” That’s a significant, if subtle, difference.

Phone interviews were a staple of Trump’s 2016 presidential campaign. It may not be immediately obvious, but phone interviews give Trump a distinct advantage in these exchanges. It’s far harder to get a word in with someone over the phone than in person, where you can telegraph your interest in speaking if not actually interrupt in a way that can’t be ignored. Stahl, sitting in the room with Trump, was able to challenge him in a way that someone over the phone could not.

As in that first exchange above. “I consider it a, so far, great achievement,” Trump said. Stahl, recognizing the importance of that qualifier, given Trump’s rhetoric on the subject, stops to point that out. And Trump is then forced to offer a bit more context. A qualifier that’s often absent from his commentary about the success of the North Korea summit.

The exchange between Stahl and Trump was littered with similar interactions. And, unsurprisingly, that was somewhat shocking to the team that’s his go-to for interviews, the hosts at “Fox & Friends.”

“It started with video of the hurricane that devastated parts of the panhandle of Florida, and the first question — it wasn’t about federal response, it wasn’t about emergency preparedness,” host Steve Doocy said, clearly aghast. “She asked him about global climate change.”

The hosts went back and forth a bit and then showed a segment of the interview.

“So if you watched the full interview, you can see, she does interrupt him a lot,”host Ainsley Earhardt said. “And people — many Republicans thought it was disrespectful and obnoxious. Many people thought it made him look better because he did answer everything correctly. But she gave a tough interview, and when you’re a journalist, you want to ask tough, fair questions. Many people had a problem, though, with the fact that she was interrupting him a good bit.”

When Earhardt sat down with Trump for an interview right after his campaign chairman was convicted of eight federal crimes and his personal attorney pleaded guilty to eight more, implicating the president, her first questions were, “How is our country’s first lady doing? And how are your children?” She later asked of the attorney, Michael Cohen, “Why is he doing this?”

Host Brian Kilmeade went back to the first subject.

“She really believes in global warming, and that’s fine. And man’s role in climate change, and that’s okay,” he said. “But I don’t think you should bring your point of view — she was trying to win over the president with her point of view.”

There’s no serious debate among climate scientists about the role of humans in climate change. People burn fossil fuels, releasing greenhouse gas into the atmosphere. That traps heat, which leads to warmer air and higher ocean temperatures, the former of which helps capture moisture and the latter of which helps rapidly power hurricanes. The question was sensible in the context, given Trump’s unique position to potentially address the climate change problem.

His answer to Stahl was a hand wave, a now-familiar “the climate has always been changing!” rhetoric that is a go-to response from those who want to acknowledge that the weather is weird but deny that humans are responsible, a sort of Brett Kavanaugh-esque “I believe something bad is happening, but it’s not my fault.” The argument itself is like saying that weather always changes from colder to warmer in the late spring, so that’s probably why the air temperature in Manchester Township, N.J., increased near the airship Hindenburg on May 6, 1937. Yes, the climate changes over the long term — but far more slowly than we’re experiencing now.

His responses on the subject were not what anyone besides Earhardt might say counted as “answering everything correctly.”

Kilmeade then continued to say that Trump could at least handle being interrupted without being offended, unlike former president Barack Obama, who would look “offended” when Fox News’s Bret Baier would interrupt him, because Obama tended to go “on and on and on with every answer.”

Baier interrupted a president? Republicans must have thought that was disrespectful and obnoxious.

There’s little question that Trump will continue to be Trump, no matter how thoroughly he’s pressed on his inaccuracies and lies. CNN’s Jake Tapper addressed last week’s USA Today op-ed about “Medicare-for-all” that bore Trump’s byline, saying that his was “only an hour-long show, we can’t get into every lie.” That’s part of Trump’s strategy: saying so many untrue things so often that it overwhelms the ability to identify each falsehood. And then there’s a side benefit, akin to the one Trump offered Stahl in 2016: The media pressing Trump on his falsehoods makes it seem as though he’s being unfairly targeted, which, of course, he’s not.

Unless you’re a “Fox & Friends” host, apparently. Earhardt tweeted the above exchange from her show about the Trump interview to her 335,000 Twitter followers on Monday morning.

“President Trump peppered endlessly with questions in an interview with ’60 Minutes,' ” she wrote. Well, yes, that’s what happens in an interview, particularly an interview with a president who is reluctant to sit down with outlets that might press him on his inaccuracies.

The response on Twitter was what you might expect. Earhardt later deleted the tweet.