Robert Freitas seemed to be trying to argue that it would be difficult, and he couldn't argue it very well - for example, he used Eric Drexler's assumptions that were conservative for Nanosystems and anticonservative for grey goo, about a single radiation strike being enough to make a nanosystem fail, in calculating the amount of shielding required for aerovores that were mostly shielding (if I recall my reactions upon reading correctly). And despite that, the best he could come up with was "the heat bloom would be detected and stopped by our police systems", like they couldn't spread through the jet stream first and go into their final reproductive phase later, etcetera.

Unless Freitas is missing something that he seemed heavily motivated to find, I have to conclude that turning the biosphere into grey goop does not seem to be very difficult given what we currently know of the rules.