Interestingly enough, I find numerous references to Clay and this incident, but very little in the way of the transcript it refers to. This was the best I could find (she is "Terminal 4"):

Judge 9: Are you familiar with Hamlet?

Terminal 4: The college kid who came home and found his mom had married the guy who murdered his dad just a little month before? You might say so.

[...]

Judge 1: What is your opinion on Shakespeare’s plays?

Terminal 4: That’s pretty general; would you be more specific? Otherwise, I’ll just say I like them.

Judge 1: Learning that you like them answers my question. Which of his plays is your favorite?

Terminal 4: Well, let’s see...Pericles.

Judge 1: Why is it your favorite?

Terminal 4: Because he was obviously called in to play-doctor somebody’s awful script. It was one of the few (maybe only two?) plays written with somebody else. It’s really rather an ucky play. What play do you like?

Judge 1: I did not understand your response. However, to answer your question, I do not have a favorite.

Fascinating! Thank you, this is definitely going on my reading list.