> The family agreed to help the police figure it out.
No. A couple of children, grand children, or cousins agreed to share their DNA (or it was legally removed without consent). The rest could have told the cops "NO", and they still would have gotten enough DNA evidence.
This. Detectives’ thirst for solving (or just finding someone to blame/force a confession out of) crimes will often override their duty for true justice, by whatever means they want.