Why can we see the earth from outer space if the sky is blue?

Well, the Earth is kind of blue when viewed from far away:

In the picture above, you see that the "edge" of the Earth is more bluish, which is due to the reason you give in your answer; here we see through a deeper layer of the atmosphere, so we see more blue light.

But the light that does reach Earth's surface is reflected back through the atmosphere, so this is seen as well. And since after all non-blue photons outnumber the blue ones, we see what's underneath the surface.