Well-- of course I'm not just going to tell anyone. That sounded private. I figured you would not wish for everyone in this place to know that, regardless of why you might suddenly have said it back there. [ Apparently he's at least that capable of reading a room..

And he also gives out these words that he won't tell anyone about what Nao said so easily - like it's a promise he doesn't even have to think about. ]

But there is nothing you can say to keep me from worrying. [ .. pause, until he realizes, well, wait-- ] Unless you wish to tell me in what way I can help you.

[ Some people might have used what Nao said for blackmail.

It seems like Inigo is going in a wildly opposite direction of that - his first instinct being to help. ]