Is there a single mob related biography, which has an explanation that is considered credible by historians? Or were they all tall tales designed to sell books?
These are all second hand accounts, but these people claimed to have heard it directly from the alleged conspirators.

Sam Giancana's brother (Chuck) claimed Sam claimed to have been involved in the murder conspiracy in his book, Double Cross.

Frank Ragano claimed Santo Trafficante confessed in Mob Lawyer.

Bill Bonanno claimed that Johnny Roselli admitted to shooting Kennedy from a sewage drain in his autobiography, Bound By Honor.

Carlos Marcello confessed his involvement in the JFK murder with an inmate, as reported by the Biography channel's Mobsters series.

You shit-kicking, stinky, horse-manure-smelling motherfucker you! If you ever get out of line over there again, I'll smash your fucking head so hard you won't be able to get that cowboy hat on. You hear me? Fucking hick. -Nicky (Casino)