I think to teach any piece, you have to know it well enough to know how the notes feel under the fingers. That means playing it through several times to figure out where the hard spots are, where the fingerings are going to be tricky, what the musical demands are, etc. If there is a recording of the piece, listening to it will help to, but is no substitute for sitting and playing through the piece yourself.
Pierre Jamet told me that anytime he judged a competition, he always learned the music well enough to understand its difficulties and form. It was no where’s near performance level, but he knew it well enough to clearly understand the piece. I think that a good teacher needs to do the same thing.