You can absolutely expect certain kinds of privacy in a public space. (Like with up-skirt photos, for instance?) The question that needs to be resolved is if collecting DNA violates people's privacy in an unreasonable manner. I think this really falls back on the question of what harm you can do to someone with their DNA.

The EFF apparently feels that you could do quite a bit of harm with it, if not today, then very soon. To me, it seems just about as bad as stalking someone.