I don't know either but I'd say that it's not outside the realm of possibility.
We all know folks whose "career goals" is to live off others, by seeking to be "injured" in some way. Sometimes it's physical (no disrespect to those genuinely injured at work) as in the old "I hurt my back" routine; sometimes it's "I was offended/insulted/harassed" (no disrespect to those genuinely harassed).
I've personally seen women outright lie about things that were said to them so I have a great deal of difficulty believing this one (particularly since we still have not had women from almost every single place Mr. Cain has been his entire adult life lining up to tell us what he did or said to them, thus demonstrating a pattern).
I also once worked with a woman who had a still-unsettled sexual harassment case pending from a previous employer. At first she seemed very believable, the quiet demure type who surely would not invite "harassment." After a couple of weeks, however, yowsa!! Her "true colors" came out and she started making a dead set after a very married male fellow employee. He worked in a different department so the contact was not constant, but this was another situation where I could see that if he outright rejected her there could have been another "harassment" charge made; I have no doubt she would have twisted things which were said. (Fortunately, she found a job more to her liking and left before it could go that far).
Maybe I'm just cynical but in my experience people lie all the time if they think they can gain from it, and women are not exempt.
Even less outside the realm of possibility that what I said.