but then again, so are II and III.
Yes and no (I think). The cameras used for shooting II and III were only 1920:1080, yes. But I want to say that the vfx and the DI were done at actual 2k cinema resolution.
IMDB confirms that, but it seems kind of silly to have a DI in a higher resolution than your filmed portions. The 2011 OT is a different beast entirely, however.