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Executives are facing sharp questions about what they knew, and an internal inquiry is reviewing why a posthumous BBC investigation about Savile’s sex crimes was shelved. The report was scrapped weeks before the broadcaster aired a series of tribute shows.

Mark Thompson, BBC director-general from 2004 until last month who is now the incoming CEO of The New York Times, is among those facing questions from U.K. lawmakers. Mr. Thompson has insisted that he never met Savile, was unaware of rumors about his behavior and had little knowledge of the cancelled expose.

In a letter to The New York Times staff on Thursday, Chairman and Publisher Arthur Sulzberger said Mr. Thompson had thoroughly explained his handling of the issue.

“Mark has provided a detailed account of that matter, and I am satisfied that he played no role in the cancellation of the segment,” Mr. Sulzberger wrote.

“Our opinion was then and remains now that he possesses high ethical standards and is the ideal person to lead our company,” the letter said.

Savile was the original host of the music countdown program “Top of the Pops,” which ran on BBC television from 1964 to 2006, featuring performances by everyone from the Rolling Stones to the Sex Pistols. For almost 20 years from 1975, Savile also made children’s dreams come true on “Jim’ll Fix It,” a TV show.

Savile championed a host of good causes, frequently running marathons to raise money. He helped to collect millions for the creation of a national spinal injuries center at Stoke Mandeville Hospital in southern England and bequeathed money for a heart unit at Leeds infirmary named the Savile Institute.

He was knighted by Queen Elizabeth II for services to charity and entertainment and received a papal knighthood from the Vatican.

Prince Charles was among those who paid tribute when Savile died last year.

David Caruso in New York contributed to this story.