Even it's ultimately possible, I can't imagine it would happen by accident. It would certainly require a lot of deliberate effort, and 1000s of new technologies.
(edit: I mean to say that there are processes that evolution has evolved that have eluded us and may continue to elude us indefinitely)
If the grey goo is non biological, there may not be any form of life that can eat it to keep its growth in check, it might also use some raw material that's more abundant than the nutrients organic life needs (there's a lot of silicon in earth's crust for instance), and it probably wouldn't have any built in limit to its replication like most living things do.
Something invented by humans is invented by natural selection. Just as new organic species can wipe out (or live harmoniously) with old species, a new inorganic species could do the same.
Because we're a lot smarter than evolution. Evolution can't make wheels or impeller pumps.
Many biological structures rely on weaker interactions (such as Van der Waals forces). Human-engineered nanotech could use the strongest covalent bonds (such as C-C bonds found in diamond), making it impossible for biological creatures to "eat" them.
In a similar vein, biology uses energy stored in chemical bonds. Humans can build things that use nuclear forces, allowing for much denser energy storage and growth far away from the sun or geothermal sources.
