Sinatra is correct. Salvie was murdered due to Chuckie Merlino's bitterness at Testa for leaving his daughter, rumors that may have been true told by soldiers such as Faffy and Tommy Del, and for his disrespect to Scarfo and Chuckie Merlino.

Salvie decided to go against authority and became "too big for his britches".

In the Mafia, that is a perfectly justifiable reason to be killed.