You apparently don't permit logical deduction, either. You'd be a terrible cop. I can see your report now:
Arrived on site. Residential neighborhood. Victim was on the ground in the street, dead, with a single bullet hole through his chest. Suspect was standing over the dead body, kicking it, and screaming I hate you, holding a gun in hand. I announced my presence and instructed the suspect to put down the gun. Suspect complied. Inspected the gun, the clip had room for two bullets. I asked the suspect if he fired the gun. He said yes. I asked the suspect if he shot the victim. He said he didn't do anything wrong. I repeated the question. Suspect didn't respond. I repeated the question again. Suspected stated he is pleading the 5th.
A witness approached. Witness stated he heard a loud argument and looked out the window. Saw suspect pointing gun at victim. Suspect screamed "Prepare to die!" There was nobody else on the street. Witness states he turned to get hisphone and call 911. Witness heard two gunshots. Witness looked back out the window and victim was on the ground. The gun was in the suspect's hands. There was nobody else visible.
I declined to arrest the suspect. Nobody saw him actually shoot the gun. He admits he fired the gun but refused to state whether he fired it at the victim. I do facts. I don't do obvious.
If further investigation is desired, I propose offering immunity to the suspect to compel his testimony as to whether he fired the gun at the victim. Case then be closed based on the suspect's truthful response.