Abstract
In a recent publication Bell and Madhukar (BM) have attempted a calculation for the adsorbate Green's function for the Anderson model. We compare their result with an earlier theory of the authors and point out that the BM result does not properly describe the strong coupling limit. Not realizing the change in the pole structure of the adsorbate Green's function for realistic values of the coupling has led BM to erroneous conclusions about the necessity of very large relaxation shifts to explain the experimental data.