Actually, the vote itself is inside, and doesn't need to be visible to the auditor. Whether the signature actually belongs to a registered voter by that name is what's being tested--and that's visible on the outside. If that's wrong, the vote is just thrown out and its vote subtracted.
But there's no violation of a voter's privacy involved. If the signature is bad, it didn't belong to a real voter. A real, registered voter's vote is not being revealed, and there's no one to harass.
At this point, the ballots have been separated from the envelopes for a long time. At best, you could identify signatures on the ballots that don’t match, and you would get a number of ballots that should not have been counted in the first place.
If that number is large enough, it could call the election into question, even though you would not know who they voted for.
You don't have to make the case to me, I'm all for it. The government argued otherwise, and the judge sided with the government. My argument is the government argued the way that it did because it never expects to be on the other side of this problem. If you never expect to be held to the rules that you're imposing on others, you'll never worry about how fair the rules are.