For anything to be 100% error free is mythological. Errors are made with every single existing manner of investigation and incarceration. A vast majority of them are correct, but sadly a few are erroneous. The directive is to use science to minimize those errors, by making the odds of making an error astronomical.
In regards to genetic science I'm not convinced that it's easy to err with the process they appear to be using. In fact I should think it's harder than with older methods, such as fingerprinting, and especially eye witnesses.
Imagine you have an unknown suspect who committed rape in locations A, B, C, D, E, and F. And you have the assailant's DNA from semen samples. By comparing the assailant's DNA to the genetic data of many people, a person is located. Now, without any other data, I would agree - this is not enough to be sure. The DNA in the database isn't complete, and you can't decisively say, "this is our man." There is no 100% comparison available. How do they know the target isn't a sibling or cousin of the assailant? But suppose the suspect they discovered also happened to live or work in locations A, B, C, D, E, and F, and had the means, motive and opportunity, and left other evidence that narrows down the odds? And suppose that he left descendants from some of those rape victims whose mother lived at those locations? With process of elimination, the odds against making an error become extremely high. Some math can be applied to calculate those odds.
Now I'm not sure who decides when the "line is crossed." I think there should be more transparency with the process and methodology so that the people whose DNA is being tapped are fully informed of how this is done, and have the option to decline participation in any database that is allowing its use for such process.
But it seems to me that the benefits (capturing numerous real murders and rapists and getting them off the street) outweighs the risk (the inconvenience of having my DNA compared to an assailant's with the very unlikely scenario that a close match might be found erroneously).