Some GLOs do not have to allow affiliations - I know my chapter voted on several affilate applications during my time there. And, if it was a large SEC chapter expecting a large pledge class - - I'm guessing they didn't want a girl they had already passed on previously AND they didn't "pick out" themselves. (Since this was a well documented "end run" around the membership selection strategy, it was probably justified not to affiliate her.)
My own brother joined a national Frat his freshman year at a smaller school, and then transferred to Ole Miss. He told me that as an "Affilitated" member, he could not vote on ANYTHING. He was simply a "social" member. But, that was the way it was organized with them.
BTW, the young woman in the discussion was actually a lovely and kind person and fit in well with the chapter on my campus, sorta leaves you to wonder WHO wanted her to join the SEC chapter . . .