I believe this to be the correct answer. He was a money maker for them and he worked for guys who were connected that were involved in the recording industry.

If he hadn't been Italian and the mob didn't have their hands in on him as an act, they wouldn't have given a fuck. Thats why they didn't give a fuck about the Rolling Stones because they were not a mob connected entertainment act. They owed nothing to the mob.

The entire Rat Pack band was owned by the Mob and they were getting a huge cut from their shows in Vegas as well. Like you said, the MOB owned Frank Sinatra. If he would have told them to fuck off he would have become trunk music. No doubt about it.