Whether murderers deserve death is a separate question to how do we know if someone is guilty of murder. We don't have a good legal system and we don't know for certain if anyone is really guilty of any crime. But we still have to arrest and punish people.
We don't have perfect knowledge. I was once accused of something I didn't do. It wasn't anything to do with the police but if it had gone before a judge and a jury they would never have believed me. If I just had the facts of the incident I would never have believed my explanation. It was ridiculous but it was also true. It caused me some trouble at the time but it is all long ago and forgotten by everyone except myself. If the accusation had been murder I would have gone to gallows laughing at the bizarreness of it. I would have accepted that the judge and the jury had made the correct decision given the facts. We live in a world where injustice is bound to happen. The best we can do is find the wisest judges and juries. Maybe we should have IQ restrictions on who can sit in judge of us.