No, that doesn't convict Joe. What that says that if Joe kills Bill, he shall be sentenced to death. It does not state under what circumstances Joe's guilt is established. If Joe did kill Bill and it is an accident, he will not be guilty of the crime and will not face the punishment. Joe has to be charged with the crime of muder, proven guilty, and then will face "a law that says any person who kills another person shall be sentenced to death".
My original point is that a parent several generations removed stated that the jury makes the law, and that is not the case. You do bring up a good point that the jury may find a law unjust and not convict because of that, but in no way do juries make laws.