The story of Ardell Sheridan and Castellano's dialog has been told so many times that it's probably true. You can understand why FFC told that story instead of the money angle--he'd like us to believe crass old Paramount cheaped out on Castellano, when in fact he had considerable responsibility for bringing the film in on or around budget.
But money talks--especially in Hollywood. If Castellano'd gotten his price, he would have been in GFII--with or (probably) without his girlfriend's scriptwriting help.

The irony is that, when GF was cast, Duvall, Caan and Pacino had yet to star in a blockbuster film, and Brando's reputation and career were in tatters. Castellano was the only bank-able star at that time, and he got the highest salary. But the tremendous success of GF made it a franchise. That "franchise" enabled FFC to have the luxury of deciding that only Pacino and Keaton (and of course, his sister) were necessary to keep the franchise going and credible. So, when the stars that he made through the earlier film(s) demanded too much, he wrote them out of the sequel(s).