...his paperballs in his mouth
Very likely. His voice was choked, and, though I heard him say "all," it could have been "no." Or perhaps he just screwed up.
But in the novel as well as in one of the original FCC scripts the surprising point is that Vito really doesn't want any inquiries. Why? If he initiates any inquiries, the other families, will get to know about it. As dontomassino said, perhaps he began already to suspect Barzini. He trusts his guts that as soon as he meets the other families, he'll find out who's behind it.
Exactly. His saying "I want all inquiries made" would be completely antithetical to what came next: "I want no acts of vengeance. This war ends now. I want you to arrange a meeting with the heads of the families..." If Vito had ordered "all inquiries made," it would be a sign to the other Dons that he was preparing for vengeance, and that the meeting he was proposing would be a trap. They'd dive underground.
And anyway, what did he need to inquire about? He
had to know that Carlo had set up Sonny, and that Tattaglia (with or without help from the other families--it didn't matter which ones since they were all at war) arranged the murder.
I believe that, even in his moment of greatest grief, Vito was thinking clearly. He recognized immediately that his top priority wazs to get Michael back safely to America to be the new head of the family. To do so, he had to appear weak to his enemies. That was the purpose of
no inquiries made,
no acts of vengeance, and the meeting. Later, in a deleted scene, Michael challenges him on not seeking vengeance for Sonny. Vito admits that "it was a sign of weakness," but to a purpose: to get Michael back, and to have Michael exact vengeance. It was Vito at his most Sicilian-subtle.
