Not sure I follow this, publicly obtained samples are not illegal, they are just not personally identifiable. If I obtain a sample from a public place, I cannot prove I obtained the sample from the person in question, but if I can prove that person has been there (i.e. they live there) and that sample is a perfect or partial match to some piece of evidence I have, than I have generated probable cause that someone in the home may have something to do with the crime. Then a judge can sign a search warrant for a cheek swab of the persons in that home, which would then be personally identifiable as the dna would be traceable from the point of collection, and this would absolutely be admissible. The man whom impregnated the woman in the vegetative state submitted his cheek swab because it was required on a probable cause search warrant of the facility employees.
I just don't think they have a good DNA sample in evidence. And I also don't think they were asking for "kitchen sink" tips at the press conference. They specifically asked to talk to anyone who saw an abandoned car at the CPS building. And when they released the new sketch they were talking to the killer and said "you never thought we'd change course and go in this direction," so there was a definitive purpose in that action. I'm not going to fall on the sword over it, but I do tend to think more than not that they have POIs for this case and the presser wasn't a big plea for tips.