I am curious about the actual false positive rate and how they compound. To use your hypothetical number, if the false positive rate is one in a million per test, if law enforcement tests your DNA sample against 700,000 samples from crime scenes, there is a 50% chance at least one of them will be a match due to false positive [1]. That is much scarier than what one in a million suggests.

[1] (1 - 1e-6) ^ 700,000 = 49.6 % chance of no false positive match