A fisheye effect working against a curve would have the effect of leveling the curve. Look at the panning sections, clarity visible distortion is taking place.
Oh. My. Goodness. This is the effect of imprecision fostered in those who live on a globe. They have no foundation and what is level is curved for them and their up is often also down. They say all manner of things contradictory like this. Fisheye lenses necessarily do not correct, but distort for the purposes of gaining more view. Fisheye lenses do not level the curve, but permit a level to be seen only when viewing directly straight on. Rather, fisheyes have been used for many years in order to curve the level. Earth is not a globe.