Studies have been done on small sections of some DNA databases, comparing every profile with every other profile, and found this to simply be false. In Arizona 65 493 profiles were made available - 122 pairs matched at nine loci, 20 at ten, 1 at eleven and 1 more at twelve. In Illinois 220 000 were checked, and 903 pairs matched at nine or more loci, and in Maryland 30 000 were checked, providing 32 matching pairs.
Add to this the problem that eyelashes, skin fragments etc can be carried on the wind, or from a random frottage, and we have some important cases being 'solved' with what amounts to deeply circumstantial evidence. With any luck this fascination with DNA being used as the be all and end all, the assayer of truth, will end as soon as possible.
You say all this as if the police walk into a crime scene having absolutely no clue who the perpetrator could possibly be, taking some DNA samples, running it through the computer, then arresting the resultant match and passing it on to the courts. In reality the list of suspects is going to be considerably narrowed by old-fashioned police work: finding witnesses, finding out the victim's history, looking for motive, etc.
In other words, fat lot of good it's going to do you to claim, "But there's a 0.1% chance that DNA isn't mine!" when you've been spotted leaving the crime scene by a witness, were seen having an argument with the victim a couple days prior, he owed you money, etc. Not to mention that if you go to find those other, say, 30 DNA matches, you find out that 21 of them live hundreds of miles away, 3 of them are in nursing homes, 1 is a kid, 2 are already in prison and have been for years...