My guess is Hy kicked back a lot of money to the Outfit in order to operate his machines in the Chicago area. I think he had his own rackets going all around the world that the Outfit was aware about but Hy operated them alone and would send back money to keep the outfit happy.
He had plenty of powerfull friends and even Corbitt stated that no one besides Hy knew how much money he was bringing in. I think Hy had the Bastones as his main contact to the Outfit.