She was saying that because of historical foreign influences and because people have immigrated to Sweden throughout history there is no such thing as Swedish culture. Which is just ridiculous.
Look, it's just some stock piece of rhetoric she learned back in the swingin' pos'structuralis' 80s, and people like her have been constantly giving similar speeches by rote ever since: "There is no such thing as X," with such things as Nature, Humanity, Reason, Truth, and Reality routinely playing the role of X in that formula. If you look through the fustian, she isn't saying that you, as a Swedish person, do not "have" any culture of your own, because that would indeed be rock-eatingly stupid and delusional. From cultural studies' point of view, it's not bloody possible for a human being to
not have a culture, because pretty much everything that human beings do and think
is culture by definition, no two ways about it. But then again, it's perfectly reasonable to wonder why some things are included in the category of "Swedish" or "Finnish" culture while others are left out for no apparent reason...
The point is that national cultures that are presumed to be monolithic and unchanging in lay discussions are
anything but for people who actually study them: It's just a simple fact that cultures change, and if you're a multi-kulti-hugs-and-kisses progressive, of course you're going to draw on facts of cultural history to argue for pluralism and diversity. Because you realize that your culture was never all that un-diverse to begin with...
EDIT: I think I'll make a dedicated thread for worthy discussion of this worthy topic...