What makes you think Cus was connected? He may have been extorted in some way and played along for his own safety but that wouldn't make him connected. I'm sure he met the likes of Frankie Carbo and Blinky Palermo at some point early in his career. They ran boxing. Based on all accounts, Cus was a good guy with the best intentions. Took Mike Tyson in as a son.

"...the successful annihilation of organized crime's subculture in America would rock the 'legitimate' world's foundation, which would ultimately force fundamental social changes and redistributions of wealth and power in this country. Meyer Lansky's dream was to bond the two worlds together so that one could not survive without the other." - Dan E. Moldea