I've seen a lady who didn't require references of me, even though she's pretty tough on screening otherwise. When I inquired about why she didn't ask (the day of the actual meeting, nonetheless) she said she talked with the other ladies at socials/gathering, and they had mentioned I was a nice fellow.
I guess my gentleman-like reputation precedes me! LOL My guess is a lot of women ask around and look at your reviews/postings to get an idea of who you are, which may forgo the need for traditional screening in some cases, but I could be wrong.