Unfortunately, that's exactly what they do. They find fingerprints and hair at a scene, and then run them through "the system" to see if they can find a match. Any matches are immediately suspects.

For certain crime scenes (like a single woman's bathroom) random bits of hair and skin from a stranger is a decent indicator that the stranger was involved with the victim in the recent past. For others, like the aforementioned convenience store, all it means is that you're a person who lives on this planet.

I would be ok with these national database if there were rules as to who could access them and for what purpose. Like you said, they need to be locked down so that only a detective who has convinced a judge that the hair or blood found at the scene of the crime is likely to belong to the suspect can push the DNA through the database and proceed to harass the 300,000 Americans that DNA will "match."

By allowing law enforcement to have a global databank of the DNA of anyone arrested for any reason (even falsely) you're allowing innocent people to be linked to crime scenes that they simply passed through. Do you know what the odds are of leaving your DNA in a place where a crime would be committed? Have you ever scratched your head in a motel room or a convenience store? Have you ever used a public toilet (or a tree on the side of the road)? The situation where the police take DNA from anyone arrested for any reason and keep it indefinitely (which, I agree with Jason, is the eventual end-game for this law) means that any shoplifter, speeder, or protester can be linked to much more serious crimes they had nothing to do with, arrested and held for the extent of the investigation, or even convicted. That's where your liberty goes. Though, as stated by other posters, that's the declaration of independence and non-binding.