Your analysis ignores the key point that bacteria operate on simple rules based entirely on local concerns, which is not the proposed case in the sci-fi story.
So you're saying that top-down management or even peer-to-peer management will exist within the grey goo scenario? I'm somewhat skeptical about top-down management, as there would be enough nano-bots within a 1cm deep layer in a city the size of NYC to far outstrip the attempts of a complex entity to control them coherently. As far as peer-to-peer communication goes, then bacteria are already doing this; http://www.hhmi.org/research/cell-cell-communication-bacteri... and they still haven't covered us in grey goo.