(CBS News) Cuban dictator Fidel Castro actually submitted to questioning by the Warren Commission following the assassination of President John F. Kennedy in 1963, a new book reveals.

The story of Castro's questioning included in "A Cruel and Shocking Act: the Secret History of the Kennedy Assassination" by Philip Shenon, a former investigative reporter for the New York Times.

Bob Schieffer, host of "Face the Nation," explained on "CTM," "It's a secret that has held for 50 years. The commission actually sent an investigator to waters off Cuba. They took him out in a U.S. Navy boat, he got onto a yacht. There was Fidel Castro and Castro had sent word that he wanted to talk to the commission and this was thought to be so controversial they didn't do it. Anyway, the investigator gets off the boat, talks to Castro, they talk for three hours. Castro says -- as you would expect -- 'No way, no how did I have anything to do with it,' and it turns out, and to me this is the most fascinating part of all, that young investigator was William Coleman, who later became secretary of transportation in Gerald Ford's administration."

"CTM" co-host Charlie Rose added, "Even more interesting he had met Castro earlier in Harlem."

"Yes, they both liked music," Schieffer added. "And he at first met Castro when Castro apparently was on his honeymoon in Harlem. They both loved jazz and they came to know each other. They weren't friends but that's why they decided it would be Coleman to do it."

In his investigation for the book, Schieffer said Shenon has done "just a magnificent job of ... connecting the dots of how the Warren Commission investigated this things."

Schieffer added that Shenon doesn't dispute the Warren Commission's conclusion that Lee Harvey Oswald was the lone gunman. In fact, he, again, underlines that there's no evidence to suggest there was a conspiracy or anybody else involved.

"But what he also makes clear is the FBI and the CIA really misled the commission," Schieffer said. "Both of these agencies were so afraid that they might be blamed because they knew of Oswald and they had been watching him in Mexico City. They just wanted to make sure their agencies weren't blamed -- they didn't play straight with the Warren Commission."

For more with Schieffer on the JFK assassination and politics today, watch his full interview above.