UPDATE 7/7: On my morning walk, I got to thinking about this. Why is it different to ask for coffee, and only insinuate an interest in sex? There are three advantages: deniability, refusability, and ambiguity.
Deniability. The speaker can protest (inwardly or verbally) that he was only asking for coffee--that's face-saving if the hearer says no. So it's an advantage for the speaker.
Refusability. The hearer can refuse a request for coffee without addressing the more intimate topic of sex. She can say--"sorry, it's too late for coffee," or some such. So indirect communication is better for the hearer.
Ambiguity. Asking for coffee leaves it open where this will lead, the open-endedness being advantageous to both speaker and hearer.
Asking for coffee in an elevator is thus clearly better than asking for sex, but the apocryphal story has taken hold that Elevator Guy asked directly for sex -- see the Atlantic story and before that, at many blogs. (For example, Amanda Marcotte reported that Elevator Guy had "cold propositioned her for sex" here.) Result: Elevator Guy's malfeasance and Rebecca Watson's victimhood have been exaggerated.
Exaggerating victimhood has a funny way of triggering exaggerated dismissal, and I think that may be what's going on with Richard Dawkins. He smells exaggerated victimhood and he says--"Bah, it was nothing!" (even though--come on!--it wasn't exactly nothing).
So I got to wondering--why does he smell exaggerated victimhood? There's nothing terribly exaggerated about Rebecca Watson's complaint in the video that started this whole controversy. She laughs and smiles as she tells the story and she quotes Elevator Guy in a way that's restrained and presumably accurate. She doesn't call the invitation a "cold proposition for sex."
Perhaps Dawkins was responding to exaggerations in the blogosphere, but I also suspect another factor. If you watch the panel on which both appeared the day before the elevator incident, you can actually see foreshadowing of Dawkins' later outburst on the web.
Watch Dawkins as Watson speaks about Paula Kirby (from about 3:00 to 5:00). Here's what Watson says about Kirby's presentation on an earlier panel about women and atheism--
She made a comment that she felt that there was no problem with sexism in the atheist community because she's never experienced any sexism in the atheist community. In the atheist community we refer to that as an argument from ignorance, and in the feminist community we refer to it as an argument from privilege. I'm genuinely happy that she hasn't experienced any sexism, but I don't think that's a proper basis to make a judgment about whether there is any sexism in atheism.I suspect this is a strawman, and Kirby didn't make the idiotic argument from "I have had no problem" to "there's no problem." She just took her experience as some evidence like Watson wants to present her experiences as some evidence.
Think about what it would be like if scientists disregarded negative data. If the question is about whether autism and vaccination are linked, studies that find no link are just as relevant as studies that find a link. Kirby should not have been dismissed as "ignorant" and "privileged."
To the extent that Watson wants to dismiss women with no negative experiences, she has exaggerated the victimhood of women. My hunch (based on his body language in the video) is that Dawkins saw her as an exaggerator of victimhood before the later video about Elevator Guy ever appeared, and that's what put him on the road to dismissal.
Moral of the story: neither an exaggerator nor a dismisser be. One tends to lead to the other. The more one side dismisses, the more the other exaggerates; the more exaggeration, the more dismissal. And also--don't claim to be the paradigm case. Women who don't get treated in a sexist manner are also entitled to tell their stories and to have them taken seriously.
Update: The Kirby panel is here, and no, she doesn't make the idiotic argument Watson attributes to her. More about her argument here.