One of the people Allen told it to was Julian Bond, who was trying to register black voters in Mississippi for the Student Nonviolent Coordinating Committee. He would later become a legendary civil rights leader.
"This was not a self-defense action by the state representative. This was out and out murder. That's all it was. But Louis Allen agreed to lie about that," Bond said.
Asked why he thinks Allen lied about it, Bond said, "He lied because he was in fear of his life. If he had implicated a powerful white man in a murder of a black man, that he was risking his life."
"Did you encourage him to tell the truth?" Kroft asked.
"I tried to encourage him to tell the truth, but you know, it was like saying, 'Why don't you volunteer to be killed?'" Bond replied.
But Allen's wife would later testify that "his conscience was clipping him" and he decided to tell FBI agents and the U.S. Commission on Civil Rights what really happened at the cotton gin. A document from FBI files says, "Allen changed his story" and "expressed fear that he might be killed."
He asked for protection, but none was provided. Almost immediately, word began circulating in Liberty that Allen was prepared to change his testimony.
"He was threatened as a result of the fact that he was going to change his statement and that he did change his statement," Deitle said.
She said the FBI was notified of those threats.
Asked if the bureau did anything, Deitle said, "Yes. We referred that to local law enforcement authorities."
"It's certainly possible to conclude that local law enforcement people were the ones behind the threats?" Kroft asked.
"There is a theory out there that that speaks to that. Yes," she replied.
In fact, it has been the prevailing theory for some time, although the FBI cannot officially confirm it. There is a 1961 reference in the FBI file to a report that "Allen was to be killed and the local sheriff was involved in the plot to kill him."
And "60 Minutes" found a 1962 letter from Robert Moses to Assistant Attorney General John Doar, alleging the same thing: "They're after him in Amite [County]," it says, and makes reference to "a plot by the sheriff and seven other men."
"He was afraid of the sheriff's department," Kroft remarked.
"I think he was, yes," Deitle said.
"And I think he was afraid of the Klan, although they seemed to be sort of the same thing in Liberty at this time," Kroft remarked.
"I'm not sure I can say that," she replied.
Julian Bond was less circumspect: "The law enforcement, you suspected they were members. If you wanted to be a mayor, a city councilman, a county commissioner, the sheriff, if you wanted to be on the legislature, you had to have some connection with the Klan."
And in the Amite County Sheriff's Department, the person with the best connection was Deputy Sheriff Daniel Jones. His father was the "Exalted Cyclops" of the local Klan, and Jones himself, according to an FBI document "60 Minutes" found, was suspected of being a Klan member.