Rhino can use both Double-prescision and single precision vertex locations for meshes.
Render meshes used for the display are Single precision. This is because graphics cards tend to take single precision mesh coordinates. So when created far from the origin they do not have enough digits to generate an accurate location. Most of the time this not a big deal as these meshes are only used for display. But sometimes it shows up.
Simply moving the objects closer to 0,0,0 will not regenerate the display mesh on the object. ClearAllMeshes removes all the render meshes from all the objects. Then Rhino will recreate the render meshes as needed. Since the objects are now closer to 0,0,0 there is more precision available.
It is covered in this wiki page: https://wiki.mcneel.com/rhino/farfromorigin