And if they are acquitted, there is no penalty or punishment assigned. That is also part of due process. If you allow the government to put the DNA of an innocent man in a criminal database, it's just a simple additional step to have EVERYONE submit their DNA - because you have trampled over due process to achieve your goals.
Due process of law means merely that -- the government cannot deprive you of life, liberty, or property except in accordance with the law. Different Constitutional provisions address which types of laws can be enacted, and which types of laws cannot be enacted.
To put this entire issue in perspective, contrast the potential abuses of DNA databases (if any) with a real life example of gross abuses of our freedom: the pervasive (and pernicious) use of progressive taxation to redistribute wealth in this country from those who earn it to those who don't -- "from each according to their ability, to each according to their needs," not in a Communist country, but right here in the USA. From my perspective, obsessing about potential abuses of DNA databases doesn't even rise to the level of focusing on the gnat on the elephant's butt.