Comment by nomel
No, they are correct, and it's disingenuous to claim otherwise. They have a DNA sample of everyone. Those samples haven't been sequenced. As you've pointed out, they are sequenced when the state needs them to be.
It would be like scanning your drivers license and putting it in a sealed envelope and claiming "I don't have your home address!", when I'm known to get the home address from other peoples envelopes when asked for it.
At least they can't trawl them for random matches when they're like that, the cost of sequencing is a barrier. Probably even more in that a 20 year old blood spot on a piece of paper isn't an ideal DNA sample.