That's just fractally wrong. The defense does not have to prove some alternate theory. The defense has no burden whatsoever.
Here's the problem: The "Oswald did it" explanation cannot be derived from the facts. It is solely derived from assumptions and conjectures made from the facts. Big difference.
And no, preponderance is a lesser standard than beyond a reasonable doubt, and is not sufficient in a criminal trial.
Calling people who don't accept handwaving and conjecture "loons" doesn't actually advance your argument.