This point is wrong in relation to the story. They have some unknown DNA, and certainly they can go and stake out peoples houses and see it they throw out a cig

This point is wrong in relation to the story. They have some unknown DNA, and certainly they can go and stake out peoples houses and see it they throw out a cigarette but or however you get it. This seems reasonable, and if they are grabbing DNA off something a person threw away, they arguably wouldn't even need a warrant. But if instead they run their unknown DNA though a database of rape victims to see if any of them was the criminal, they're not "just taking a sample", they are invading the privacy of vulnerable women on the off chance one of them is a criminal. And they are obviously deterring people from reporting future crimes in which they have to give their DNA. I don't believe I need to belabor this, the case in the story had nothing to do with how easy it might be to collect DNA from someone you've already identified