The reference paper is actually not really wrong, just poorly communicated for this physics audience. If you read the paper this letter is responding to, it becomes clear that the authors are referring to the probability distribution of an incoherent sum of the referenced orbitals. The letter to the editor sloppily writes (emphasis mine)
We therefore must describe the electron as (to use chemically familiar language) a “resonance hybrid” of $2p_x, 2p_y,$ and $2p_z$. In more detail, we write if $ \psi = \frac{1}{\sqrt{3}}(2p_x + 2p_y + 2p_z)$ and this is exactly a spherical distribution, as Johnson and Rettew have shown.
Where, out of context, every physicist assumes that the author specifically means a coherent sum of wavefunctions, and where both the wavefunction and the probability distribution resulting from it are not spherically symmetric. However, I believe (I'm no chemist) to a chemistry audience the common phrase "resonance hybrid" would immediately imply an incoherent superposition of the given states, as there's nothing particularly coherent about normal chemistry. The word "distribution" also hints that something is funny, as it's not typical to call the wavefunction itself a "distribution". Specifically, Johnson and Rettew showed that $\psi_{2p_x}^2 + \psi_{2p_y}^2 + \psi_{2p_z}^2$ is spherically symmetrical, which it is. Since there is basically only one equation in the referenced article, this is clearly what Cohen was referring to. The phrasing of the letter to the editor could clearly should have been clearer here, but good communication does take effort from both sides, especially when the two sides come from different fields where notation is not so well standardized or understood.
For completeness, if a shell is partially filled then there's the possibility of there being a specific angle between the orbits of electrons in the inner shell and the electrons in the outermost shell (think, e.g. of two concentric donuts rotating independently). Even in a mixed state, the outermost electron would be in a mixed state of interacting with various orientations of inner electrons, none of which are independently centric, which suggests that assuming a central field approximation will miss some important physics.