I think the character said "no inquiries made". It doesn't really make any sense for Vito to have said "all inquiries made".

As he said "This war stops now". Vito wanted to be able to bury his first born son and mourn in peace. He wanted to be able to bring back his youngest son. He finally wanted to seem to give in to the Five Families while plotting a revenge that would take years to bring about.

So he didn't want any of his people , especially Clemenza, who was Sonny's godfather, nosing around upsetting the apple cart, by asking questions and thus indicating to their enemies that the Corleone Family was by no means willing to let bygones be bygones.

Anyway although the Family leadership may not have initially known that Barzini was behind Santino's murder, they all immediately knew that Carlo was. So there really would have been no point to any further inquiries. The Don already had all the information he needed.

"When the snows fall and the white winds blow, the lone wolf dies but the pack survives."
Winter is Coming

Now this is the Law of the Jungle—as old and as true as the sky; And the wolf that shall keep it may prosper, but the wolf that shall break it must die.
As the creeper that girdles the tree-trunk, the Law runneth forward and back; For the strength of the Pack is the Wolf, and the strength of the Wolf is the Pack.