"Since you are so concerned about the interactions of clothing with probability theory," Ougi said, "it should not surprise you that you must wear a special hat to understand."

But isn't this almost the exact opposite of what the student was saying? Questioning the robes indicates to me that the student felt there was not any interaction between learning probability theory and clothing, and that therefore it served some other purpose, presumably differentiating between an in group and an out group.

Or am I just nuts for trying to argue with you about the internal thoughts of your own fictional characters?