So the cops have a suspect for a burglary and want DNA evidence, but they don't have enough to get a warrant, so what do they do? Well, they just stop him under the pretense of administering a DUI test, and then keep the saliva he leaves on the machine as "abandoned" property. Certainly, a court we see straight through this sham and reprimand the police who tried to pull the stunt, right?
So the police can't order you to give them a DNA sample directly, but they can order you to do something that gives them a sample indirectly, even if they order you to do it merely to get said sample. Make sense? Thought not.