By all means, use your no-rec. It sounds like this girl is disturbed--she is a criminal if she skinned a cat--and would you want this kind of person in your chapter?
I have only used my no-rec twice. This past year, I used it for a PNM whom I worked with this summer and truly believe to be mentally disturbed because she physically attacked other employees. My daughter, who's the kind who never wants to say bad things about acquaintances, sent one to the AOPi chapter at that school as well...she worked with her too. The chapters did a little checking on their own and called to thank us.
I wouldn't use my no-rec casually; however, there are times when you have to actually protect the Greek system.
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