"And even when you think you perhaps understand the causation bits, you still have no idea what on earth that Persian stuff is about!"
I've always thought that it would be roughly equivalent to "I believed something without ever having any direct evidence, and now I see that the belief was accurate". Essentially, that the student finally demonstrated conclusively that he understood the process behind the responses of Zen teachers.
But there are probably multiple levels of interpretation, of which that is only the most obvious.
From "Hyakujo's Fox", #2 of the 49 koans in The Gateless Gate:
Mumon's poem:
It really makes you wonder how the hell they got that far while still believing that the wrong answer could turn you into a fox.