The father's DNA was in the database because he had a criminal record. […] They didn't randomly take a test of just every person

Not totally random but: law enforcement uses Ancestry (et al) DNA data. To be clear, it's not back-channel access, these are publicly available databases. But it can get weird. There was a case a few years ago where police showed up at a guy's door looking at him for murder because his father's DNA (which was in an Ancestry database) was a strong match for a crime scene sample, which meant his DNA was a strong match, which made him a strong suspect. And IIRC there was a similar case where the suspect was the Ancestry user, but the actual perp was his uncle who he barely even knew. Those were quickly resolved, but still. Had not considered that.

The people in those databases are there voluntarily, but their family members aren't. Ether way you wouldn't think of Ancestry DNA as a law enforcement database. But it might be. And those services are getting really popular. It's really only in its infancy right now.