I suppose that would be so, Jace, although I was never close to my paternal grandfather, and all the stories I heard about him were from my father, who told them after his father died. .Probably he wasn't much in Lanza's company. James Caan, on the other hand, had an FBI file opened on him after Joe Colombo agreed to let him hang out with Persico's crew to "learn their style" during GF filming.
I'm sure you know the story about how Lanza started the ball rolling on using the Normandie fire to get Charlie Luciano out of prison.