It wouldn't be their finest hour, but it might add an intriguing chapter to the history of perhaps the greatest British dynasty of the 20th century. A middle-aged woman from the American Midwest claimed this week to be Winston Churchill's illegitimate grand-daughter.
Rhonda Noonan, a 54-year-old inhabitant of Tulsa, Oklahoma, has spent 30 years trying to track down parents who gave her up for adoption as a newborn. Her conclusion: that she was fathered by our wartime Prime Minister's only son, Randolph.
The allegation divides historians who have examined Ms Noonan's claims. Some believe that it has the ring of truth. Others caution that the evidence is at best circumstantial.
Both groups agree that the only way to confirm or deny her genealogy is via a DNA test. That move is currently being blocked by the Churchill family. They will not co-operate with Ms Noonan.
She recently enlisted the services of a Hollywood PR man, Michael Sands, who worked with Randolph Churchill's late daughter, Arabella. He hopes that publicity will force the Churchill family's hand. If not, then Ms Noonan is at work on a memoir.
"I have spent half my life researching this, so I don't have any doubt about who I am," she told The Independent on Sunday. "It's an epic story. But of course I know that it will take a lot for most people to believe it. That's why I want this DNA test."
Ms Noonan's tale begins when she decided to track down the parents who had given her up for adoption in 1956. After a decade spent sparring with the state's Department of Human Services she won a court order in 1990 forcing them to give her a copy of her birth certificate.
From this, she traced her biological mother, Irene Pruitt-Gaffard, who by then was 76 and lived in the nearby city of Purcell. But the elderly lady refused to identify Ms Noonan's father, or discuss the circumstances under which she was conceived.
Then Ms Noonan accessed the original case notes from her adoption file, which mentioned her father had been British, and contained handwritten addendums suggesting that he was well connected and that his identity had therefore been hushed up.
About 10 years ago, Ms Noonan called former employees of the state's adoption agency hoping for more information and received an anonymous tip identifying her father as Randolph Churchill. "It explained so much about me and the way I am. I look just like Randolph Churchill. I cock my left eyebrow just like he did."
The eminent Englishman, had visited Tulsa around the time Ms Noonan was conceived. A correspondent for The Times, he was covering the Democratic nomination in the presidential race.
During the trip, Ms Noonan discovered, Churchill spent several nights at the officers' bar at Tinker Airforce Base. She believes he met Irene Pruitt-Gaffard there, and a romance ensued.
Though no documents back up her theory, she has a statement signed by Polly Hunt, a now-deceased employee of the state adoption agency. She claims to have been involved in the adoption and the cover-up of her father's identity.
Members of the Churchill family have been contacted by Ms Noonan but none has replied. If Randolph was her father, her closest relations would be the four offspring of his son Winston, the late Tory MP, or Arabella's two children.
The only relative to respond to inquiries this week was the author and journalist Celia Sandys, the daughter of Randolph's elder sister Diana, who would be Ms Noonan's cousin. "I am aware of this," she said. "But I have no wish to comment."
That leaves expert historians. Winston Churchill's biographer, Professor John Charmley, the head of history at the University of East Anglia, believes there is "nothing inherently impossible" about Ms Noonan's story.
"Randolph was in the US at the time, and he was quite capable of a one-night stand ... [he] was a womaniser." Regarding Ms Noonan's appearance, Professor Charmley added: "There's a resemblance, and if one looks at older photos of Randolph, a definite one."
Another Churchill scholar, Richard Toye at the University of Exeter, said he was "highly sceptical". "Without a DNA test, her story will convince no one, except a Hollywood agent."
The person who could have unlocked the mystery is now uncontactable. Irene Pruitt-Gaffard, who changed her name to Pat Nail, died on Friday, in Purcell. She was 96.