The gulf between what people say they want and what they actually do (whom they ask out, or from whom they will accept requests) is vast. Self-reporting is largely a matter of public relations. People who refer to evolutionary psychology as "evo psych" are dog-whistling for the tabula rasa crowd and can be safely ignored; you can't tell them anything they don't want to hear anyway.
In any case, your worst suspicions are likely to be true. Men did the asking out, by and large. Men were bigger on the shotgun approach, also no surprise. We asked people to rate each preference as to how important it was to them ("do you really need blue eyes?") and women, on average, rated all of their preferences as more important than the men did. Height was almost always in the top three for women, in terms of preferences, in terms of whom they asked out if that did happen, and from whom they would accept requests. That and income.
I've seen other studies, later, which bore all of this out, but if you want the true dirt, you go look at what people actually do, not what they want someone to think they do.