<p>Sooo...it's only sort of programming related, but I figure it's election day, right? Is there a single good reason why they aren't, not necessarily open source in that anyone can contribute, but open source in that anyone could inspect the source?</p>

the problem is opensourcing the software would be a no-op.
They don't have any decent cryptography, and there has been demonstrated and relatively easy ways to contravene them simply by hot-swapping a ROM chip in the voting booth, or Having a device that augments the records in the record cartridge.
Youtube: Sequoia Part 1 Those with access can hack with programmed ROM chip
Youtube: Sequoia Part 2 Logic and Accuracy Test vs Election Mode with vote-stealing firmware
Youtube: Sequoia Part 5 Manipulating Sequoia Voting Results Cartridges from Precincts
@Mnementh
The bad cryptography and the possibility to swap the ROM-chip has nothing 
  to do with open-sourcing the code? So there is the point?
There are only 3 logical reasons for opensourcing this code:
To put under scrutiny how the votes are counted to be certain its doing it right.
For somebody to be able to modify that code for their own needs.
To put the software into public domain so public committers can improve on it.
Points 1 and 3 are blown out of the water in terms of usefulness and "proving your vote counts" because you have no assurance that the code you are seeing/improving runs on these devices.
So that leaves only condition 2 being useful, and as you are not going to
own
your own voting machine, and have no need for one for anything more than nefarious causes
or
to simply prove their vulnerability.
For the majority of cases all it would mean is that there would be more information publically available on
how
to contravene these machines, so you would no longer need physical access to one in order to attempt reverse engineer their software and develop compromised ROM chips for use in said devices, grossly reducing the barrier to entry for the compromise of the voting system.
Granted, even in a non-opensource state this information can still leak, and you just have a false sense of security because you assume "theres no leak, I am safe", but on the contrary, if you open source it people will assume "hundreds of people have looked at the source code, I am safe" which is an equally bad false sense of security.
People are looking for a silver bullet safe way of voting, and sadly, there is none. Not without growing a race of purified peoples whom are brought up by non-committal monks in isolationist shrines to have a breed of people simply for the task of witnessing and counting votes accurately, whom are trained to be amoral and can't be bribed to switch the vote.
( It would sort of be like the 'dark angel' series except with voting agents instead of assassins, and we all know how that show works out, one of them would go rouge, we'd trust them, and they'd screw us all )