The electronic structure of the low-dimensional 4d⁵ oxides Sr₂RhO₄ and Ca₃CoRhO₆ is herein investigated by embedded-cluster quantum chemistry calculations. A negative tetragonal-like t_2g splitting is computed in Sr₂RhO ₄ and a negative trigonal-like splitting is predicted for Ca ₃CoRhO₆, in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longer-range crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t_2g ⁵-t_2g⁴e_g¹ couplings via spin-orbit interactions produce in Sr₂RhO₄ 〈Z〉=〈〈ili·si〉 ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d⁵ spin-orbit-driven oxides such as Sr₂IrO ₄. On the other hand, in Ca₃CoRhO₆, the 〈Z〉 values are lower because of larger t_2g-e_g splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the 〈Z〉 values that we predict here, the importance of many-body t_2g-e_g couplings mediated by spin-orbit interactions, and the role of low-symmetry fields associated with the extended surroundings.