[VadeRetro]

This is, of course, a mis-use of the word "to know." What your friend is saying is: "I feel that it's true."

You know he didn't know; I know he didn't know. But he didn't know he didn't know.

[PatrickHenry]

You know he didn't know; I know he didn't know. But he didn't know he didn't know.

I know he didn't know. He didn't know how to know. (But you knew that.)