> With one satellite, you won't get a circle on the earths surface, but a sphere.

With one satellite you get a sphere in 3D space, but if you are on a surface (like that of the Earth), that gets translated into circle.

If you are in a plane in the sky (3D space), then you get a spherical 'location fix'.

True. But the GPS receiver doesn't know whether you are on the surface or not (and at what elevation), so it must always assume 3d space, hence a sphere.