Her argument, though I can't do it justice in a paragraph, is that sex for women can be bad, very bad, with a guy who has the 'wrong' personality. Men reading this may not realise, but some other guys are truly awful in bed (like upsetting and painful). So anonymous sex is very much a minority interest among women - I've never done it for instance, and I don't know many women who have. The risks are too great, and the potential pay-off too unreliable. You don't think it out in those cold terms, but you know it in your heart. For men the risks and rewards show less variance, so anonymous sex is a better 'bargain'.
I think this explains some of the inexplicable stuff I have read about sex - the definitions of 'casual' and 'anonymous' are elided, sometimes in the same conversation, and people end up talking at cross purposes.
I think - BTW - if men realised how much young women are interested in relatively casual sex with men who are considerate and non-scary in bed, then there'd be more fun sex to be had. Which can only be a good thing.
ETA, as well as picking apart the definition of the word 'casual' the discusson which folows picks apart the word 'sex'.
as long as you define sex only in terms of men having orgasms, and not mutual pleasure, you are going to have more men than women wanting what you have just defined. Furthermore, treating fact that women want sex that is defined only in terms of male orgasm less than men as proof (...of various stereotypes...) is self-defeating.