That's not a bar that's reached in the vast majority of criminal cases tried in the United States, or anywhere else for that matter, so it seems odd (approaching disingenuous) to try and establish that level of certainty here.
If the American justice system doesn't attempt to prove that the person actually conclusively commited the crime and has mens rea as well as a motive and a congruent time-frame to commit it, then something is terribly wrong.