Wow, it had never occurred to me that the government might establish mass, passive DNA collection. Sort of reminds me of the East Germans and their little scent jars... Would the government have to tell us if they had collected our DNA through passive means in public?
Just kidding.
That would require a conspiracy on a scale never seen before that is just not possible considering how poorly coordinated governments are and would be stupid to do because if it were to be found out by the public would end in mass revolt.