What initially looked like a disaster for Ben Carson could now be a major black eye for Politico.

On Friday, Politico reported that Carson had "fabricated" his application and acceptance into West Point, and that his campaign had acknowledged as much in an interview.

That story was initially headlined "EXCLUSIVE: Ben Carson admits fabricating West Point scholarship." It seemed like the sort of story that had the potential to ruin Carson's ambitions for the presidency.

But the Politico story was not accurate on some key points.

And in the wake of pushback from the Carson campaign -- which called the story an "outright lie" -- Politico softened its headline, removed the "fabrication" language, and changed some key details -- even as it said it was "standing by its story."

In a statement, Politico said, "We stand by our story which is a powerful debunking of a key aspect of Ben Carson's personal narrative. The story online includes additional details now as well that bolster this account."

The rewritten article did not initially include a correction or editor's note, although a note was later added on Friday. Politico again said it "stands by its reporting."

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But Carson's campaign sees the matter differently: "It's clear that what the Politico writer, with what he was trying to gain with the headline, did not substantiate it with his article," Armstrong Williams, Carson's business manager, told CNN's Wolf Blitzer.

Politico's initial story began by stating that Carson's campaign had admitted "that a central point in his inspirational personal story was fabricated: his application and acceptance into the U.S. Military Academy at West Point."

In fact, there is no evidence in Politico's story that Carson ever claimed to have applied to West Point.

The Politico story does show that Carson said several times that he was "offered a full scholarship to West Point." He made that claim in his book, "Gifted Hands," and in several media interviews, including during an appearance on Charlie Rose last month.

Carson acknowledged Friday that he was never offered a full scholarship to West Point, and sought to clarify that he had instead been given an informal offer or "nomination" to attend West Point.

"Because I had done so extraordinarily well you know I was told that someone like me -- they could get a scholarship to West Point. But I made it clear I was going to pursue a career in medicine," Carson told The New York Times. "It was, you know, an informal 'with a record like yours we could easily get you a scholarship to West Point."

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Politico also claims that West Point "has no record of Carson applying, much less being extended admission." But West Point told CNN on Friday that it does not keep records of decades-old applications, and would not be able to know if Carson was offered an appointment because he did not attend.

Finally, Politico's story seeks to cast doubt on Carson's claim that he was introduced to General William Westmoreland during Memorial Day of his senior year at high school.

In "Gifted Hands," Carson writes that his high school ROTC director "introduced me to General Westmoreland, and I had dinner with him and the Congressional Medal winners."

Politico says official U.S. Army records show Westmoreland did not visit Detroit around Memorial Day in 1969 or have dinner with Carson. "In fact," Politico reports, "the general's records suggest he was in Washington that day and played tennis at 6:45 p.m."

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But Politico goes on to note that there was a similar banquet event in Detroit in February of that year that the General did attend, and that "Carson, a leader of the city's ROTC program at the time, may have been among the invited guests at the $10-a-plate event."

Following pushback from the Carson campaign, Politico softened its headline and changed its lead and various details in the story. The story is now headlined, "Exclusive: Carson claimed West Point 'scholarship' but never applied."

Carson's campaign, meanwhile, seemed unfazed by the report. Barry Bennett, Carson's campaign manager, said in an email to CNN that the story had been "debunked."

"Ben was offered a nomination which he declined," Bennet wrote.

Editor's note: The author of this story was a reporter for Politico from 2011 until September 2015.

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