If the Earth is flat and of finite thickness, then we have to take on board the points raised earlier about asteroid/comet collisions and the Earth staying flat. There are a few possible resolutions to this problem:
1) The Earth is extremely thick, making impacts of any magnitude negligible
2) The Earth is extremely massive, making its moment of inertia extremely large (same effect as 1)
3) Some combination of the above
4) The DE/UA/whatever forces the FE to be level for some reason (equilibrium point)
or, otherwise
5) The Earth is infinite and as such as infinite moment of inertia (in the limit that an impact doesn't cause a hole/fracture)