The closest we had to a rude PNM when I was active, was a psycho PNM.
It was my sophomore year, my first time rushing on the other side and the first time our local had been allowed to participate in FR alongside the 4 NPC sororities. It was pretty obvious that we were a Jewish sorority (when the sisters have last names like Rosenberg and Segal, it's a dead giveaway) so a lot of non-Jewish PNMs dropped us.
However, "Jenny" figured she was a shoe-in because she was Jewish and we were the smallest chapter on campus - how could we
possibly cut
HER????
She was invited back to two chapters for the first invite-only round. At the time, chapters made their own name tags for PNMs, and PNMs were allowed to keep the tags. Jenny went to XYZ first, and then came to us wearing her XYZ-issued name tag (a no-no - you can keep the name tags but you're supposed to pocket them). The message was obvious - rush me hard or I'm pledging XYZ. I spoke with her and it took me about five seconds to determine she would not be good for our chapter. Still, I was polite to her ...
She was cut by both chapters before pref.
She came to our informal rush later that semester. We cut her again.
She found her home in a service org - so, good for her. Still, *cough*nutcase*cough*