There are no tidal forces involved in the phenomenon described.
The article clearly says if you jump you will take longer to come down; that isn't a tidal effect. A tidal effect would be that the wrinkles on your face form more slowly than the wrinkles on your toes, or that water splashed into the air will form slightly more elongated bubbles during this alignment. [AND ... Neither of these things happens because even with planetary sized bodies tidal effects are, within experimental error, entirely first order effects.]
The -2 in the -2dr/r is not a tensor. The expression is just the differential: d(2Gm1m2/r2) Unless you're claiming that scalars are tensors. OK, they are. But no actual physicist calls a scalar a tensor. As a matter of fact the first order term in the expansion is a vector, and it points radially, and again, nobody but the prissiest mathematician on the planet actually calls a vector a first order tensor.
In any event, you are simply wrong. This article talks about a "tidal" effect to give it an air of authority, but the effect described is not the least bit tidal. It's simply a gravitational effect, and about 15 orders of magnitude smaller than claimed.
Au contraire, it's the only thing that COULD be involved, because of the free fall principle. The earth and everything on it, could free fall at any rate with out our noticing it. It is only the differential rates of fall, or attraction, that could cause objects on the earth to separate from each other.
This phenomenon is discussed in detail in treatments of objects falling into black holes. Of course, the claim here is supremely ridiculous, because the magnitude of the effect claimed would imply very strong tidal forces.
The -2 in the -2dr/r is not a tensor.
I said, "The "-2" in -2dr/r is the -2 in the tidal tensor ..."
... IN the tidal tensor, you see. That tensor is represented by the matrix:
1 0 0
0 1 0
0 0 -2
Recall the tensor maps a vector to a vector, and this tensor maps a displacement vector ( from earth center ) to a force. The -2 maps a z displacement to a force in the z direction, and derives from the differential that you wrote down.
I know this stuff! Believe me!