Hello Swedpat, I know how you feel about all this as I used to misunderstand this physical notions too, here's how it works:
Field flatness is the relative flatness of the transversal image given by the instrument, it useally is spherical which means that the plane of focus is actually not a plane but a portion of a sphere, therefore you cannot have simultaneously perfect focus in the centre and in the edge of the FOV (think of a tangential plane to a sphere), you need "to bring" the edge to your focal plane. Flat field instruments fix this problem, all the areas of the FOV are sharp because the field is closer to being a plane, BUT it doesn't mean that the field is not distorded (think of a distorded picture in a flat frame), distortion is actually a deformation of the image, flat does not mean without distortion, I know it can be misleading.
You can have a flat field with distortion and a curved field without it.
FLATNESS IS NOT ABOUT THE CURVATURE OF THE IMAGE, BUT ABOUT THE CURVATURE OF THE FIELD!
Now the rolling ball effect of the SV (barrel distortion "amplified" through scanning) has been GREATLY exagerated in this forum, it has become a fashion talk by snobs who don't know what to say to stand out from the crowd.