That whole bit was adapted by FFC and Puzo from real life--in this case, from a celebrated war within the Joe Profaci Mafia family in Brooklyn ca. 1959-62. As has been posted here many times before:
Joe (Joe Jelly) Gioelli set up some gambling operations in Profaci territory without paying tribute to Profaci. Profaci ordered the Gallo brothers (Larry, Crazy Joe, Albert) to whack Jelly, and promised them Jelly's games (territories) in return. They whacked him, Profaci welshed. So the Gallos kidnapped several of Profaci's hierarchy and held them hostage. Profaci appealed to the Commission. The Commission ordered the hostages freed, and Profaci to make good on his promise to the Gallos. They released the hostages, Profaci welshed again. So the Gallos split off and went to the mattresses. The matter came to an end when Larry Gallo was lured to the Sahara Lounge in Brooklyn after-hours. There he was garotted by Profaci soldiers, but a policeman happened by and broke it up. The NY Daily News printed an unforgettable photo of Larry being led away by cops, with a big red circular abrasion on his neck.
Profaci later died of cancer. His successor was his brother in law, Joe Magliocco. He conspired with Joe Bonnano to whack Carlo Gambino and Tommy Lucchese. Joe Columbo, a capo in Magliocco's family, ratted out the plot to Gambino. Magliocco was called before the Commission, paid a fine, was forcible retired, and then died of...a heart attack. Columbo was made new Don of the Profacis.