In, oh, 34 years of writing recs, I think I've written 2 or 3 "no" recs. I don't really remember the reasons now, but I'm pretty sure they were fairly lurid.
There have been girls I was, um, reluctant to sign on. Not because they were so awful, but because I really didn't think they would fit into the chapter, or there were grade problems.
When that happens, I send in the rec as an information-only form and ask the chapter to call me before recruitment starts. I can then tell them my concerns, and let them make their own decision.
Back when I was a collegian, we pledged a girl who had a "no" rec because the alum didn't like the town she was from. Another "no" on a girl that the alum felt would not complete college. In both cases, we should have listened to the alumnae!
Another chapter pledged a girl who had serious mental and emotional issues. There was no rec on her from the alum in charge of getting recs for that high school.
Why?
Because the chapter didn't bother to ask the alum for a rec.