When President Trump proposed the awarding of a “fake news trophy,” he exempted Fox News from consideration because, as he has said many times, he views the network as one of the only media outlets that covers him fairly.

But the president appeared to take a rare shot at Fox News on Thursday when he complained about a “very false” article.

Trump briefly answered questions from a small contingent of reporters in the Oval Office before a meeting with Irish Prime Minister Leo Varadkar, including one inquiry about whether he would make additional staff changes.

“The story was very false,” Trump said, without identifying a specific story. “I mean they wrote a story about staff changes today that was very false. We made a wonderful change. I think Mike Pompeo is going to be an incredible secretary of state. We have some wonderful ideas. ... There will always be change but very little. It was a very false story. It was very — a very exaggerated and false story.”

There have been many reports in recent days about the prospect of further shake-ups, but clues suggest he was talking about one from Fox News, in particular. Trump, as evidenced by his Twitter feed, often begins his day by tuning in to “Fox & Friends.” Counselor to the president Kellyanne Conway appeared on the show on Thursday morning, and this is how the interview began:

STEVE DOOCY: I'm going to read you a headline on FoxNews.com right now, and then we would like the answer to it. It says, “McMaster, Shulkin and Kelly could be next to go in White House bloodbath, sources say.” Of course, what they're talking about is Rex Tillerson being shown the door a couple days ago. Mike Pompeo is the president's pick. What's going to happen ...

AINSLEY EARHARDT: And Kelly is General Kelly, not you.

DOOCY: That's right. So, what — are there going to be more changes? That's the first question.

CONWAY: I don't have any personnel announcements. I have to say I'm just fascinated with all the stories about palace intrigue and personnel and a lack of stories about policy. It really is amazing. Thank God the president himself goes out across the country, like he did for two solid days this week, and takes his message directly to the people. ...

And I'm sorry, folks, but let me just say I'm going to focus on the policies here and leave personnel to the president. I will tell you it is a privilege and blessing to walk into that building every single day and serve the country we all love. If you're low-distraction, high-production, you'll do very well here, and you'll last the strongest and the longest, if you'd like to.

DOOCY: Sure. Well, Kellyanne, you know we cover the policy. We talk about what the president does every day. It's just — but this has been a big week for personnel changes, given that. And that's why there's this speculation.

Based on what we know about Trump's media habits, there is a good chance that he was referring to Fox News when he said, a short time later, that “they wrote a story about staff changes, and it was very false.”

Though Trump often praises Fox News, he did complain about its coverage early in the 2016 Republican presidential primary. And he might have been inclined to do so again on Thursday because the “Fox & Friends” hosts took the unusual (for them) step of challenging Conway's spin.

Doocy did not point out the irony of Conway — she of “alternative facts” and multiple ethics violations — saying the key to longevity in Trump's White House is to be “low-distraction.” But he did push back against Conway's contention that the media's priorities are out of whack.

Notable exits since Feb. 28 include White House Communications Director Hope Hicks, chief economic adviser Gary Cohn, Secretary of State Rex Tillerson and President Trump's personal assistant, John McEntee.

It is pretty hard to argue that the recent turnover, which fits a pattern, does not warrant the extensive news coverage it has received. Plus, Trump himself seemed to foreshadow more replacements when he told reporters on Tuesday, “I'm really at a point where we're getting very close to having the Cabinet and other things that I want.”

“Close” — as in not there yet.

Moreover, Conway's complaint about “all the stories about palace intrigue and personnel and a lack of stories about policy” is inconsistent with the Reagan-era axiom that “personnel is policy.” Trump, of course, is an ardent admirer of Reagan, campaigning on a pledge to “Make America Great Again” (a slogan previously employed by Reagan) and saying that the last time America was great was during the Reagan administration.

For multiple reasons, Conway's argument rings hollow. And perhaps the strongest evidence of its hollowness is that even “Fox & Friends” wouldn't go along.

It appears that Trump, unaccustomed to such resistance from opinion hosts on his favorite channel, delivered a glancing blow in return.

This post has been updated.