Your first guess is immediately correct, but somehow the officers and investigators don't even bother to properly interview or investigate the person who is clearly the murderer. That's not the fault of the series though, so that isn't why I rated this episode so low. With about 20 minutes still left in the episode, the episode reveals the (obvious) killer, and reveal his confession. And yet, the episode slogs along for another 20 minutes adding nothing to the story. For the last 20 minutes, it's just painstaking tedium about looking for the body, and how the family doesn't believe that the body they find is the actual missing person. It's a painfully drawn-out episode, one that can be skipped.
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