While there can be some debate about the accuracy of current DNA sampling techniques and database matching techniques, I have little doubt that this technology will improve to the point it can perfectly tell if two people are not the same, and that they are the same. It's a great deal more detailed than fingerprints. Indeed, before too long DNA samples will allow them to produce a decent physical description of you.

As such, in considering these issues, I am looking at the long term view, when the tech becomes even better, though until it is, we should be wary of mistakes as you say.