I just realized: if the Anti-SOS
is going to be a mirror-image of the real SOS, they're not only going to need Anti-Haruhi, but also Anti-Kyon.
Imagine that for a moment.
But then I don't think it's a true mirror image anyway. I'm not sure if I'm forgetting something, but other than the members of the SOS Brigade, who are together only by Act of Haruhi, I don't think we've seen
any indications of the three factions (aliens, ESPers, time travellers) working together, or even being civil enough to give the time of day to each other.
This seems to be a bit of a change from the Other Side, who appear to want to work together for whatever reason. It's also entirely possible that they're acting of their own accord, without active direct orders from their superiors. Then again, the counterpart to Yuki's boss seems to prefer eschewing interfaces completely.
It's interesting that (as far as I remember) two of the three of the faction representatives in the SOS Brigade have told Kyon that if they were to be given orders that would go against the SOS Brigade, they might well revolt, and stay on the side of the SOS Brigade against their faction. The one who
hasn't, in my recollection (again, I could just have missed it), is Mikuru the time-traveller.