Then along came DNA testing. It has tossed uncertainty out the window, most recently with the help of a former president's grandniece who spoke to CNN's "New Day" on Friday.
The same technology that confirmed the source of a stain on Monica Lewinsky's blue dress has now made its way into the history books to air the laundry of another president, Warren G. Harding, who served from 1921 to his death in 1923.
Harding's descendants persistently denied the claim until this year, when his grandniece Abigail Harding and grandnephew Peter Harding decided to it was time for accountability. They owed it to Britton's descendants, Abigail Harding told "New Day."
"One thing that everyone deserves to know is who they are, if they can. Where they come from. Who their ancestors are," she said. So, she and her cousin, Peter, contacted Jim Blaesing, Britton's great-grandson.
"His family was nervous and very mistrustful, and they didn't want to be hurt," Abigail Harding said. There were also misgivings from some of Harding's descendants. "One branch of the family ... was opposed to digging up the past."
But Peter and Abigail Harding wanted to know, and Blaesing was eager to vindicate his ancestors' claim of the relationship. So, Abigail, who had already done a genetic profile with Ancestry.com suggested Blaesing do the same.
"Right before the results came back, we had a little nagging fear, you know, what if the results came back negative," Abigail Harding said. Then she got a message to her Ancestry account. "It said, 'You have a second cousin,'" she said.
The tests indicated kinship with 99.9% accuracy. Blaesing called her. "The first thing he said was, 'Hi, cousin.'"
They are shooting for a family get-together in March.
President Harding's lovers
The revelation of the love child did not besmirch a pristine reputation, as Harding has not been a stranger to scandal. And Britton was also not his only mistress.
Harding already had to manage his reputation after marrying Florence Kling De Wolfe in 1891. She was a divorcée, which was frowned upon in polite society at the time, and many considered it adultery.
But during his marriage and parallel to the affair with Britton, Harding was also seeing Carrie Fulton Phillips, the wife of a store owner in Ohio. They were lovers from 1905 until 1920, just before Harding took office, according to the Library of Congress
Last year, the Library of Congress confirmed their affair beyond a doubt, when it released their love letters, which contained salacious details.
Harding may have written similar letters to Britton, but she claimed she destroyed them at his request.
Harding's political scandals
Then there were the political scandals of the Harding administration.
Secretary of the Interior Albert Bacon Fall secretly leased federal oil reserves to big oil companies, triggering what became known as the Teapot Dome
scandal. Shortly thereafter, Harding received word that political friends were using their positions in government to enrich themselves.
His health declined, and Harding died of a heart attack while traveling in the West with Secretary of Commerce Herbert Hoover.
After Harding's death, Nan Britton was confronted with the cold fact that he had made no provisions for the care of their daughter, Elizabeth Ann.
Partly to raise money, Britton took her story public a few years later with a titillating book titled "The President's Daughter."
It described love romps with Harding, and said that he set her up in a house in New Jersey when he was a senator. Elizabeth Ann was born in October 1919, not in a hospital, but in that dwelling, Britton wrote. Everything had to stay under wraps.
Harding secretly sent her money for support, the book claimed.
But Harding's family scorned the book and the woman, and much of the public came down on the side of the deceased president's reputation. Britton was branded a liar.
So it stood for 90 years, and the story was handed down through Harding's lineage.
"We had always [all] our lives been told -- it wasn't true -- that Nan released that book for smear purposes, that Harding had mumps and was sterile," Abigail Harding said. "I said OK, and I'd repeat that answer -- I remember -- when people were asking."
But Britton's book fell into the right hands generations after she wrote it. Peter Harding read it. Abigail Harding had collected it as a bit of presidential memorabilia.
"Peter said to me, 'You need to read this, my gut feeling is that she's telling the truth,'" Abigail Harding said.
The positive legacy
She doesn't condone her presidential ancestor's behavior, but she doesn't condemn him either. "A lot of presidents have had dirty laundry, and we didn't hear about it so much. But it's out there," she said.
Rumors of infidelity followed Lyndon Johnson, John F. Kennedy and Dwight Eisenhower, she pointed out.
They all did good things in office, and so did her presidential ancestor, she said. His lack of conventionality may have helped.
Harding supported women's right to vote, presided over an economic recovery after the Depression of 1920-21, and worked to smooth over relations with Latin America. And he was the first president to speak out in the South on behalf of civil rights for African-Americans, according to the University of Richmond.
On a stop in Birmingham, Alabama, in 1921, Harding praised African-Americans for their service in World War I, which had ended a few years earlier. And he affirmed they were politically equal under the Constitution.
"Let the black man vote when he is fit to vote; prohibit the white man voting when he is unfit to vote," he told the crowd. When he called for an end to prejudice, black listeners, relegated to a segregated section, broke into cheers.
"He was pretty ahead of his time," Abigail Harding said.