I guess my wife is technically "the person I'm currently sleeping with," but that characterization is awfully rude and condescending.

You're absolutely right about Prudie's bias, but don't let that prevent you from recognizing your own.

She can indeed invite whoever she wants. Sometimes it's fun to bring spouses, partners, or even casual dates; other times it's not. As a noob, she should recognize that she has options, as well as many future opportunities for parties of all stripes. And of course no one should show up uninvited and unannounced.