Seems to me like the man's being played for a fool in your original scenario.
Culturally there's a lot of ideas floating around about how men ought to protect women--which is cool, I guess, but it leaves out how women can protect men, too. Traditionally it made a lot more difference than men are stronger--not so much now, what with the availability of lawsuits and (if things get really bad) guns. Of course women have always protected men by waging the information war in the circles of gossip and reputation. Well, it changes with the culture, but that's the way it often is.
There are many kind-hearted men who still buy into the idea that men should protect women, rather than simply people protecting each other, mostly because it gives them an opportunity to do something they feel good about. To be someone else's rescuer makes people feel strong and heroic, and that's a good feeling even if it does come from a silly cultural cliche. Men feel more pressure in that respect than women. (Though, women feel more pressure to be caretakers, even when it takes much more resources than they've got, so maybe we're even when it comes to unrealistic expectations in that area. I figure eventually we're just going to realize that everybody can rescue and/or take care of everybody else, and gender doesn't really have to play into it; nor should it make the other person indebted to you or implicitly inferior to you.)
But that's beside the point. A woman without a conscience could probably take advantage of a man's tendency to want to come to people's rescue--maybe even by implying that she'd want to date him if he did so. Though--I hope she doesn't go out with him after all, because she sounds like someone you'd want to steer way clear of. Ironically, she's using the idea of the male as "strong rescuer" to capture power for herself--but in such a way that I couldn't condone it no matter how much I want gender equality. Such an immature person isn't ready for a relationship.