I'm a closet Judge show fan. You should really go on it, for all the reasons already mentioned, and also put that woman in her place regardless of her demeanor.
I hate to sound repetative, but only go on if you think you'll win, otherwise closet Judge show fans will think you're a dweeb. Just remember not to interrupt, man that pisses me off.
A friend of mine went on the show a while back and said she was acting in terms of hating her best friend. free trip nukkah!