That being true, I am very leery even of the basic "doesn't respond with a height requirement" part of this anecdote.
I have seen a lot of dating profiles with things like "no short guys please", "minimum height 6 ft." etc; and have heard a lot of my female friends openly admit to "not liking short guys". For some reason, admitting that seems to be a lot more socially acceptable than a man admitting that he doesn't like women with a certain body type.