Idiots saying it's black and white, you are all assuming the man who -murdered- another man is telling the truth about why he murdered him.
Based on the evidence at the scene of the crime the police believed his story. I really doubt the cops simply listened to what he had to say then decided everything is okay and walked away. They more than likely did investigate the scene of the crime. If they even have a small suspicion you're guilty they'll arrest you without hesitation.