I believe the ties between Genovese family and the Outfit goes even back to the Five Points gang.
Thats probably right.
IMO Johnny Torrio is still underrated in the history of American Organized Crime/
I agree @H. After his adventures in Chicago, he probably went with Luciano, Adonis and the Genovese family, including with some of the old non-Ital leaders which in fact was a sign of the "Chicago way". And if you ask me, the best example regarding Torrio's respectability and stature is when he arrived in Chicago as peacemaker regarding the conflict between Ricca and Accardo (1954 i think).
Mongol General: Conan, what is best in life?
Conan: To crush your enemies, see them driven before you, and to hear the lamentations of their women.