The truth is, you might have already given it. You shed your DNA - your hair, your skin cells, your saliva, your sweat - everywhere you go. So if someone wants your DNA, they got it.
It is another question what people would do with it. As of today, I can think only of organ donation, but easier to deal with cloning... or go the route of stem cells.
As to the police "framing you" for the crime you did not commit, well, put yourself in their shoes. They need to find the serial killer and possibly, something else, who killed the two Delphi teenagers.
If they arrest someone else for it, and later the killings continue, and then someone, somewhere, catches this guy and they find out someone was framed...god saves them, because the LE is really in a tough bind. With the whole state of Indiana, because I can't imagine the sum of the lawsuit. OMG.
I made all my kits open for LE in Gedmatch, except for people who did not. I did not fight with them, I said, OK. I wonder what happens if one day, one of my relatives, matches some profile... but put it like this, if my relative is able to kill two kids, or be the serial killer, I am unsafe under the same roof with these people, too, because they are clearly psychotic.