Then again, I guess we've seen that you literally cannot be too paranoid.
You don't have to have "everyone's DNA on file". It's actually pretty trivial even for your neighbor or whoever to get your DNA.
As for the police falsifying evidence, there's a wikipedia-long history of cases, in Europe, Latin America, Asia, etc. Especially in politically charged times, like the sixties and seventies. Heck, something like half of Italy's government in the 70's have been proved in later Italian courts to be involved in such things.
Sorry, I wasn't clear. I can dump a gallon of your blood and semen onto a dead guy in an alley, but how would the government trace that blood and semen back to you?
Well, as the culprit, you can always arrange some things or leave other stuff that also points to me.
Also, your main benefit is that the police will more easily believe that it wasn't you (since your DNA won't match).