I think that's only half the story though. You're probably right that you'd get extra noise from averaging the two smaller pixels than from a large one, but that's only the whole story if you're shooting a flat color.

For any object with a shape and edges, the extra resolution also gives you better shape definition, and the resampling to a smaller image may give a nicer anti-aliased edge that using the lower res sensor. Since images often have areas with edges AND areas of flat (or nearly flat) color, you need to find the resolution/noise sweet spot for the imaginary "average picture".