It could have been a simple story of facts, exaggeration and fetal tissue. In the last Republican presidential debate, Carly Fiorina passionately challenged Hillary Clinton and President Obama to watch one of the undercover videos featuring a Planned Parenthood official talking about donating fetal tissue to researchers.

Describing the videos at last week's debate, Fiorina said, "Watch a fully formed fetus on the table, its heart beating, its legs kicking while someone says we have to keep it alive to harvest its brain."

It was arguably her best moment of a very good debate performance, but fact-checkers pointed out quickly that none of the videos — by the Center for Medical Progress — actually showed this.

Other campaigns have climbed down from similar claims about the videos. Fiorina and her allies have done no such thing. Three days after the debate, CARLY for America — the PAC that legally has to keep its distance from Fiorina's actual campaign — put together a video that spliced the candidate's answer with different clips. The viewer, hearing about the controversy but unaware of the original videos, might think that Fiorina nailed it.

In this ad by the Carly for America super PAC, Republican presidential candidate Carly Fiorina fires back at the media for questioning the existence of a video showing an abortion she cited during the second Republican debate. (Editor’s Note: This video contains graphic content.) (CARLY for America/YouTube)

Today, Planned Parenthood responded to the clip, faxing a takedown request to Fiorina's campaign office — not the PAC. The confusion was understandable, as CARLY for America skirted the kludgey rules around the naming of super PACs by turning the candidate's name into an acronym: Conservative, Authentic, Responsive Leadership for You. And the family-planning group's fact-check stands on its own. Planned Parenthood notes that one photo actually portrays "a Pennsylvania woman’s stillborn son, which was used without her permission and falsely passed off as an aborted fetus in an earlier video" by the Center for Medical Progress; the video of a kicking fetus comes from "the discredited Grantham Collection, an old anti-abortion archive based in Florida"; the audio splices together three different CMP stings.

"This fake video doesn’t show what you have claimed," Dawn Laguens, executive director of the Planned Parenthood Action Fund, writes in the letter to Fiorina. "Simply put, the video you described at the debate does not exist, and the video you’re now asking people to watch is not what you claim it is. This fraudulent video is beneath a serious candidate for the presidency, and you should take it down immediately."

Laguens ends the letter by inviting Fiorina to "visit a Planned Parenthood health center, learn more about the full range of services it provides." Fiorina's campaign, initially confounded by why it was asked to respond to someone else's video, has declined. (CARLY for America also was thrown and directed The Washington Post back to the Fiorina campaign. The Center for Medical Progress did not reply to a request for comment.)

"Carly is a cancer survivor and doesn't need to be lectured on women's health by anyone," said Fiorina's deputy campaign manager, Sarah Isgur Flores. "Over their long and factually incorrect letter, Planned Parenthood doesn't and can't deny they are butchering babies and selling their organs. This is about the character of our nation."

Conservatives, by and large, have sided with Fiorina on that final point. Several chimed in at the Federalist, a conservative news site that previously excoriated Neil deGrasse Tyson for misrepresenting a quote from George W. Bush. Since the Republican debate, the site has published several stories arguing that "fact-checkers" were subjecting Fiorina's video claim to a ridiculous test.

"While it is obviously not the same baby as the one she harvested the brain of, the footage helps viewers to understand what a 19-week old baby looks like when hearing the testimony of an ex-employee who harvested brains from babies of the same age," argued the Federalist's Mollie Hemingway. "Illustrating stories with appropriate images is a common journalistic technique, one used by all media outlets."

Jonah Goldberg used his column in the L.A. Times (and National Review) to make a similar argument. "The exact scene, exactly as Fiorina describes it, is not on the videos," he conceded. "But anybody who has watched the videos would find Fiorina’s off-the-cuff account pretty accurate... the video Fiorina probably had in mind included eyewitness descriptions accompanied by borrowed footage of a fetus dying in a metal bowl, its leg kicking, to illustrate the witness’s recollection of seeing precisely that in another case. That sort of juxtaposition might not fly on the nightly news, but it’s the sort of dramatic device used in documentaries all the time."

Fiorina has had no trouble explaining to conservative voters that the mainstream media is simply trying to put one over on them. Last Thursday, after "Good Morning America" anchor George Stephanopoulos pointed out that no CMP video described exactly what she said it did, Fiorina said she had "seen the images" to which she had referred.

"Honestly, I went on national television the morning after the debate, and George Stephanopoulos told me I was mistaken, that the tape doesn't exist, that the images aren't real," Fiorina told the audience the next day at the Heritage Action policy summit in South Carolina. "Well, yes, they are real."