But let's say the Input->Output is reproducible all the time with no chain between the voter and the result. You /still/ have no way to ensure that the checkbox corresponded with the name, and that you cast the vote you think you did. Perhaps this is outside the scope of the article, but its a fairly glaring deficiency.
Perhaps I'm misunderstanding. But all you can tell with this system is that "your" ballot went into the magic box and a (presumably reproducible) result came out the other side.