Well I wouldn't assume the story is accurate - obviously she wants to make a good story. So applying for "identical jobs" might have some poetic freedom in it.
In any case, if she went to see the client face-to-face or by phone, all sorts of other things might have happened. She might have fared better on average than a man. There is no way to tell from her story.
It really is just a story, all sorts of other parameters could have affected the outcome. What sort of thing is she writing? Some subjects might be more readily associated with men, other with women.
The choice of names could have an effect in all sorts of ways, not only by signaling a gender.
Really, there is no substance here at all, I am sorry. If people want to get worked up about that story, it is because they want to get worked up about it, not because there is real substance.
For a better experiment, take the one with randomized CVs with randomized names, where black sounding names fared a lot worse than white sounding names. That is a proper experiment, because all other things besides the names were equal. This story here is not science. She herself is drawing a conclusion from her experience, but her subjective explanation doesn't really explain anything.