Odd/Even swap rule for chiral compounds in stereochemistry
While this rule is certainly not infallible, it is often used in organic compounds, especially for Fischer projections.

The odd/even rule implies that no change of configuration occurs if an even number of swaps are made at a single chiral center and change of configuration occurs if an odd number of swaps are made at a single chiral center.

Here, you have made 3 swaps at both ends which means you changed the configuration of 2 out of 4 chiral centers. Hence, you can make the inference that 2 chiral centers (C-2 and C-3) are the same, while another 2 (C-1 and C-4) are different. These are hence diastereomers.

I am assuming that you thought you made 3 + 3 = 6 swaps, so the compound should be identical. But the odd/even swap rule is only applicable to a single chiral center, hence the error.

Finally as pointed out already, this rule doesn't apply anywhere where the central atom doesn't have a tetrahedral geometry. As counterexamples, coordination complexes often have non-tetrahedral geometries:

octahedral: $\ce{[Co(NH3)6]^3+}$
square planar: $\ce{[PtCl4]^2-}$
dodecahedral: $\ce{[Ce(NO3)6]^2-}$

Note that these specific examples are optically inactive but by changing the ligands for different ones, it is possible to create optically active versions with the given geometries.
However, since organic chemistry mostly involves tetrahedral carbon as the chiral center, the rules certainly do apply there.