Flat Earthers: How do you explain Google Earth?

In case it's not apparent from the title of this post, I don't subscribe to the flat earth theory. I am fascinated, however, by the number of followers and the effort they put into their beliefs.

So I ask you this: How does Google Earth work? Consider the following logical statements:

1. Google Earth maps Earth's surface onto a sphere that I can rotate and otherwise navigate.
2. I can verify that places I have been around the world (e.g. Australia, USA, NZ) are represented correctly with no distortion.
3. A circular plane cannot be mapped to a sphere without massive distortion.

If the flat earth theory holds true, then I would expect large parts of Google Earth to be mangled beyond recognition. What's the deal there?

Cheers!