I'm not quite sure - why would "only a copy" be different from "he is the android"? Surely being a copy means being identical, I mean.
Then again, the machinery must be capable of some fine-tuning, as it made the second Kirk willing to engage in deception and actions directed against Starfleet and his friends, even when it retained all of his wit and charm and initiative. We don't really know of a reason why Ruk would fine-tune Korby... But Ruk had initiative of his own, and might have seen it useful to turn the copy of Korby into a passionate fan of the Old Ones and of android existence, while the original Korby might not yet have possessed those qualities.
Ultimately, we're left wondering whether the Kirk copy was in any way related to the Korby copy, or the henchmen copies. After all, Kirk was made of a lump of goo, while Korby and his assistants had circuitry and mechanisms inside them, just beneath the skin. Did that goo transform into mechanisms inside the second Kirk, too? Or were there mechanisms inside the goo all along? Those of the Korby bunch being so close to the skin make that a bit unlikely, as the lump wasn't Kirk-shaped to begin with, but that's something we can easily handwave away.
Timo Saloniemi