Congratulations, you have just found the meaning of covariant derivatives. What your article simply says is, that, if a particle's world line has a non-zero second derivative (coordinate acceleration), this does not mean that it is undergoing an acceleration (physical) yet. But, if the first derivative is zero, then, certainly, both the physical and coordinate acceleration are zero.
However, the point you were making is that the Earth is not accelerating, but we are. My point still remains valid. If, in any frame of reference, the world lines of a point of an object on the Earth and a point on the Earth itself have different accelerations, whether coordinate or physical, it does not matter, then after a finite amount of time their relative position will be changed, i.e. there will be relative displacement between the two. This does not happen.
Now, please don't use some 'exotic' terms and try to look smart. Instead, answer in a straightforward manner the simple question:
If the effects we call gravity near the Earth's surface are caused solely by the acceleration of the Earth relative to some inertial frame of reference, then why are these effects the same on the upper and lower hemispheres of the Earth? By upper and lower I mean the hemispheres obtained by cutting the Earth's globe by a plane passing through the center of the Earth and being perpendicular to the acceleration vector of the Earth.