Hoover's FBI tapped King's telephones from 1963 through 1966, based on the pretext that King was being influenced by Communist interests. Robert Kennedy, at his perch as attorney general, approved of some of the initial surveillance of King's inner circle.
Hoover kept a steady stream of damaging information about King flowing to both Kennedy brothers.
Historian Michael Beschloss said Hoover appears to have been trying to manipulate the Kennedys to turn on King, by sharing tidbits -- like his supposed snickering at JFK's funeral -- that he knew would resonate with Mrs. Kennedy.
"If there was anything that was going to turn her instantly against someone, that was it," Beschloss said. "She was furious at Martin [Luther] King, at what she had heard he had said about her husband's funeral. And so, when she found out about what may or may not have been on these tapes, she was extremely ready to believe that there was some terrible things there."
Mrs. Kennedy's recollections of her husband's feelings toward King were far warmer. She said he went out of his way to emphasize he wouldn't "judge anyone" based on what he was told about the FBI surveillance.
"He said what an incredible speaker he was during that freedom march thing," she recalled.
King met with Kennedy at the White House when he was in Washington for the march, just months before the president's assassination. And his phone call to Coretta Scott King after her husband was sentenced to jail just weeks before the 1960 presidential election was an event some historians credited with boosting black turnout -- possibly handing Kennedy the presidency.
Mrs. Kennedy seemed to reference that call on the tapes, but she didn't finish her thought.
"He acknowledged that having made that call during the campaign got them -- Then he told me of a tape that the FBI had … ," she said.