Hill was referring to the mid 50's when the Mob was very strong. In November, 1957 they held a national sitdown in upstate New York (Apalachin) which was raided by NYS police, and soon became a fiasco for the Mob. The meeting was organized by Vito Genovese who was trying to announce himself as the "Big Boss", and to "introduce" Carlo Gambino as the boss of the Family that would soon bear his name (Gambino, backed by Genovese, had the former boss, Albert Anastasia, killed the month before the meeting).

The line about Joey Gallo taking on a boss was a reference to the Gallo/Profaci Wars in the late 50's/early 60's in which Joey Gallo and his brothers were a disgruntled faction in the Profaci Family who sought more money and power from their Family leader (Joe Profaci). This story was the basis for the Rossatto Brothers/Frankie Pentangeli war in "Godfather - Part II".