The TDKS and LR-TDDFT approaches are formally and operationally equivalent in the limit of a weak perturbation to the ground state, provided that the full basis of o × v excitation vectors is employed in the LR-TDDFT approach. As such, TDKS calculations reveal the true TDDFT spectrum in the absence of any truncations. This might be important in characterizing how the CVS approximation impacts Land M-edge spectra and for this reason we investigate TDKS calculations of XAS in the present work, beginning (for simplicity) with elemental K-edge spectra. In so doing, we discovered that a recently reported "intruder state" problem appears to be ubiquitous and pervasive in high-quality basis sets. This issue renders the TDKS approach unusable except in a modified form that is described herein.