"I guess kirin are a little like the Exalt then, in a sense.." The sense that they're connected to the gods and kind of carrying out the will of the gods. Except the communication back where Inigo is from is usually a little more direct than that. It's the benefit of being able to awaken Naga and actually talk to her in times of need.

Inigo doesn't say more though, which leaves the road way open for Tidus to pave it with his own questions if he so wishes. Apparently this whole story is just a lot less odd to Inigo at this point.