"Deke" Deloach says he never saw anything other than friendship between the two men, but that Hoover was aware of rumors.
"He's actually said to have agents go and visit people and say 'I understand you're talking about the director,'" said Braver.
"I did," Deloach said. "I was told to do it, saying, 'You have made remarks concerning Mr. Hoover being a homosexual. Give me the evidence.' And they'd always back down."
Through the years, under eight presidents, Hoover became so entrenched that he was all but untouchable.
LBJ allowed Hoover to serve beyond the 70-year age limit. He signed an executive order exempting him from compulsory retirement for an indefinite period of time.
And Richard Nixon didn't fire him, either. "Nixon was afraid to do it," Deloach said.
"Were people afraid to do it because they were afraid Hoover would go ballistic on them and start leaking out bad stuff about them?" Braver asked.
"That was part of it. They were afraid of him."
Hoover died in 1972 at age 77.
His funeral was a state occasion. But shortly after his death, details began leaking of a controversial domestic spying program, known as COINTELPRO, and of Hoover's own personal abuses - for example, using FBI agents to work on his home.
"What do you think happened to Hoover along the way?" asked Braver.
"Hoover, being as powerful as he was and having all this adulation all the time, did think he was God," said Kessler. "Initially he was very far-sighted. He did create this great organization. But as time went on, he became a despot."
Shortly after Hoover's burial, Clyde Tolson, who inherited Hoover's entire estate, bought the closest available plot. And almost 40 years after J. Edgar Hoover's death, we are still wondering about his secrets - Those he used, and those he kept.
For more info:
- "The Secrets of the FBI" by Ronald Kessler (Crown Books)