(CNN) After more than five years of touting "birther" conspiracy theories, Donald Trump on Friday finally conceded a simple truth: "President Barack Obama was born in the United States."

He did not apologize or speak to his own role in spreading the falsehood, which many people see as an attempt to undermine the legitimacy of America's first black president. Instead, Trump offered a curt admission tainted by yet another demonstrably false charge: that Hillary Clinton and her 2008 primary campaign "started" the racially charged smear.

Both FactCheck.org (working with CNN's Jake Tapper) and PolitiFact have refuted the suggestion on multiple occasions. But the revisionist telling that Clinton was somehow involved persists, thanks in large part to Trump. He has peddled it for years and is now promoting it to deflect attention from his own leading role in advancing the lie.

Here's a look at the underlying disputes:

Did Trump just conjure this allegation against Clinton out of thin air?

Not exactly. The claim predates Trump's interest in promoting birtherism.

One of the first documented questions about Obama's provenance came in early 2007, when the right-wing Insight Magazine reported that researchers with ties to Clinton's campaign were trying to make hay over his schooling during the years he lived in Indonesia. The Clinton team denied this.

The rumor was that Obama attended a madrassa, or Muslim religious school. The connotation, at least at the time, would be that he had been educated in Islamist or radical anti-American ideology.

But even then, there was no suggestion Obama had been born outside the US.

What have Clinton and her allies said publicly about birtherism?

There is no evidence that Clinton in 2007 or 2008 bolstered, supported or much less "started" the birther crusade.

And in recent years she has repeatedly blasted it, calling the movement "insidious" in a speech to supporters during an NAACP dinner in May. Last September, speaking to CNN's Don Lemon on the "Tom Joyner Morning Show," Clinton called the idea that she created the birther rumor "ludicrous."

"First of all," she added, "(the birther claims are) totally untrue. And secondly, you know, the President and I have never had any kind of confrontation like that."

Going further back, President Bill Clinton in May 2010 denounced birtherism as a "myth." During their primary battle and shortly thereafter, before Obama nominated her to be secretary of state, Hillary Clinton mostly faced questions about Obama's faith. Her denunciations of that whisper campaign weren't quite as robust as her current language about Trump and the birthers, but she never elevated either falsehood -- and certainly was not to blame for starting them.

But what about claims that top Clinton aides were involved?

Proponents of this allegation tend to point to a memo, written by Clinton pollster Mark Penn, and a conspiratorial email forwarded by a pair of campaign staffers in 2007.

Penn's internal note was titled, "Lack of American Roots," and painted media reports about Obama's time as a child in Hawaii and Indonesia as having exposed "a very strong weakness for him -- his roots to basic American values and culture are at best limited."

He wrote: "I cannot imagine America electing a president during a time of war who is not at his center fundamentally American in his thinking and in his values."

However unsavory the sentiment, Penn, who is not working for Clinton's current campaign, did not at any point address Obama's birthplace.

Clinton never pursued Penn's notion as a line of attack. Later in the year, the campaign dismissed two staff members in Iowa who passed along an email that cast Obama as a Muslim agent bent on "destroying the US from the inside out."

"Our campaign does not tolerate this kind of activity or campaigning," spokesman Mo Elleithee said at the time . "As soon as it came to our attention, we asked (the second emailer) to step down." On Friday, Clinton 2008 campaign manager, Patti Solis Doyle, denied outright any role starting the movement.

The campaign also responded in 2008 to allegations, made by Matt Drudge, that "stressed Clinton staffers" were circulating a photo of Obama wearing a turban with a blanket denunciation

On Friday, the former Washington bureau chief for McClatchy, James Asher, tweeted that in 2008, Clinton associate Sidney Blumenthal told him "in person" that Obama was born in Kenya. Blumenthal denied the claim to CNN's Dan Merica, saying Trump "is the one who embraced and promoted the birther lie and bears the responsibility for it."

CNN has attempted unsuccessfully to reach Asher for comment. He told his former employer, McClatchy, Friday that he met with Blumenthal in 2008, and that the newspaper chain dispatched a reporter to Kenya to investigate. Nothing came of it. He said there already had been stories published with the allegation before that meeting.

Some 2008 staffers told CNN that Blumenthal was not officially part of the Clinton campaign, and a CNN check of Federal Election Commission records shows no payment to Blumenthal from the campaign.

What did she say about the birther allegations -- and their forerunners -- back then?

In 2007 and 2008, the birther conspiracy mostly took a backseat to another bogus tale -- one that suggested Obama, a Christian, was secretly a Muslim.

During a March 2008 interview with "60 Minutes" correspondent Steve Kroft, Clinton said she had no knowledge of the rumor promoted by Drudge. Kroft then asked, "You don't believe that Senator Obama's a Muslim?"

This is a transcript of their subsequent exchange

Clinton: "Of course not. I mean, that's, you know, there is no basis for that. You know, I take him on the basis of what he says. And, you know, there isn't any reason to doubt that."

Kroft: "And you said you'd take Senator Obama at his word that he's not a Muslim."

Clinton: "Right, right."

Kroft: "You don't believe that he's a Muslim or implying? Right?"

Clinton: "No. No. Why would I? No, there is nothing to base that on -- as far as I know."

Kroft: "It's just scurrilous --"

Clinton: "Look, I have been the target of so many ridiculous rumors that I have a great deal of sympathy for anybody who gets, you know, smeared with the kind of rumors that go on all the time."

But Clinton's use of five words -- "as far as I know" -- prompted outrage from many Obama supporters. Critics argued that they left the door open for unsavory innuendo.

Could Clinton have been more forceful in pushing back on the rumors? Yes.

Is there evidence that she or top campaign officials stoked the fire that Trump and assorted right wingers have openly and gleefully fueled in public for years? No.

So why is Trump trying to blame birtherism on Clinton now?

Trump's decision to backtrack on the birther issue -- and pin it on Clinton -- is likely a campaign tactical move designed to improve his standing with moderate voters who might be susceptible to charges that Trump is racist.

According a CNN/ORC poll from September 2015, 80% of adults said they believed Obama was born in the US. Less than half of the dissenters chalked it up more to their suspicions than the presence of any legitimate evidence.

The same survey found that 61% of Trump's own supporters did not subscribe to birther rumors, so the campaign likely considered that it had more to gain than to lose by dropping this as a wedge issue in his race against Clinton.