You can't know which final ballot was your vote, but you can know that your ballot was in the mix coming in, and that the mix going out wasn't altered (within some probabilistic bounds).
I think this is the part I don't understand. Partly because I don't know anything about mixnets, and it feels like its paradoxical. But if that's how it is, then I can accept it.
Well the voter can verify if the voting machine is acting honestly by querying the salt used for encryption (refer to "How do you know your ballot was properly constructed?"). From an adversarial voting machine's perspective the chances of the voter validating the ballot is 0.5 and given the sensitivity of the elections, I'd imagine even one incident of foul play spreading like wildfire to raise alarms
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.