Media ethicists and watchdogs are criticizing CNN for conditioning the anonymity of a private citizen on his speaking and acting in a way approved by the multi-billion-dollar news network.

In an article published on Independence Day, Andrew Kaczynski, senior editor of CNN’s KFile, tracked down the Reddit user who made a short video mocking CNN that President Trump gave wide circulation to in a tweet on Sunday.

Mr. Kaczynski declined to reveal the video-maker’s identity — citing the man’s apology, remorse and fear of reprisal — but said CNN “reserves the right” to do so in the future “should any of that change.”

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Indira Lakshmanan, Newmark Chair in Journalism Ethics at the Poynter Institute for Media Studies, said attaching conditions to an average person’s privacy is “strange” and “troubling” behavior for a news organization.

“What I find troubling is the sentence that says, ‘CNN reserves the right to publish his identity should any of that change,’” Ms. Lakshmanan said. “Why? I don’t understand that sentence. I’ve never seen that in a story before.”

She said she had no problem with CNN finding out who made the video, equating posting online comments to standing on a soapbox and shouting in the public square.

“Just because you want to use an alias and an anonymous handle doesn’t mean that, if what you say becomes newsworthy and gets picked up and tweeted by the president, that you don’t suddenly become news,” she said. “Yeah, you become news.”

“But the strange thing is saying we reserve the right if you return to your previous behavior,” she continued. “That is strange. That I don’t understand. Why not just say, ‘This person asked not to have his name released, and we complied’?”

CNN denounced the president Sunday after he tweeted the video, which depicted Mr. Trump at a World Wrestling Entertainment event from 2007 tackling a man who had CNN’s logo superimposed on his face. The network said the video would “encourage violence against reporters.”

Brent Bozell, president of the Media Research Center, said CNN overreacted to the video.

“This is CNN that has been so embarrassed, it has overreacted so badly to that silly ‘Smackdown’ video — which I wish the president hadn’t done — but they’ve overreacted so badly by suggesting that it’s fostering violence against the media, that they’re trying to find the upper hand on this,” Mr. Bozell said Wednesday on Fox Business Network’s “Varney and Co.”

CNN ignited a firestorm on Twitter on Tuesday night when they published the article, with figures ranging from Donald Trump Jr. to WikiLeaks founder Julian Assange weighing in on the controversy.

Sen. Ted Cruz, Texas Republican, said the Atlanta-based company may have broken a Georgia law prohibiting extortion.

In a statement Wednesday, CNN said any “assertion that the network blackmailed or coerced him is false.”

The article is just the latest black eye for a network that has emerged as Mr. Trump’s favorite “fake news” punching bag.

Last month, CNN was forced to apologize and retract a report saying the head of a Russian investment fund, who met with a member of Trump’s transition team before the inauguration, was under congressional investigation. Three senior journalists at the network resigned over the story, which CNN said did not meet its editorial standards.

In the following days, Project Veritas began releasing undercover videos from its “American Pravda” series showing CNN producers and on-air personalities questioning the network’s nonstop coverage of Russian interference in the presidential election.

Conservative radio host Rush Limbaugh said it’s the “end of CNN.”

“You turn the criticism on them, and they can’t handle it,” Mr. Limbaugh said on his show Wednesday. “They can’t even handle being laughed at, much less being criticized. And now they’re applauding themselves for their great investigative work in uncovering and exposing this poor guy who made the video of Donald Trump body slamming the CNN logo.

“They clearly do not know how to deal with Trump,” the radio commentator said.