It probably sounds more like "here" than "her." But I do not much like the banning of hero/princess playing. What you should do is simply not enforce or judge the roles. If a boy wants to be rescued by the girl, that's perfectly fine, and just as valid as the boy rescuing the girl.
I'm not Swedish myself normally boys are "ham" and girls "hende", so yes it was some kind of englishfication for the sake of argument.
I follow the thought in these experimental kinder gardens in Sweden. However just as limiting as gender stereotypes are, they are very important also for a small child testing different relations and self conception. To stay in such a self image for the rest of your life is sad though. As we are talking about women here, the leading characters in "Sex and the city" would be an example of that kind of arrested development.