The Earth's diameter is ~13000 km. Surface area is therefore 4 * pi * r^2 = 4 * pi * ((13000/2)^2) = 500 million square kilometres (which is, as you say, about 200 million square miles).
I suspect the parent is both confusing a million with a trillion and also miles with kilometres.
Neither. It's just such a habit to type miles. I meant 510 trillion square _meters_, which google and wolfram alpha tell me is correct.
In any case.. the reason I chose that is because that's probably close to a reasonable maximum single pixel resolution for tracking imagery. I wanted the scope of the problem to be obvious by choice of units; unfortunately, I screwed that part up. :(
I suspect the parent is both confusing a million with a trillion and also miles with kilometres.