The resolution of the apparent paradox is that the Kohn-Sham energy is not calculated as the expectation value of the Hamiltonian in the Kohn-Sham wave function. The moment we adopt the Kohn-Sham approach, the original Hamiltonian of the system is no longer relevant. We are dealing with a reference system that is no longer interacting, but the rules for calculating the energy from the orbitals have also changed and are now expressed in terms of the exchange-correlation energy functional of the density. One could argue that the "particles" of this reference system are the "quasiparticles" of the original system, and this may help to rationalize the a priori surprising success of the Kohn-Sham orbitals in predicting single-particle excitation energies.