Empirical abundance maps derived with the help of Zeeman Doppler mapping are found to be at variance with the predictions of numerical models of atomic diffusion in magnetic atmospheres of ApBp stars. Although theory has often been made responsible for this lack of agreement, direct spectral synthesis based on the published abundance maps reveals that all the chemical inhomogeneities claimed for HD 3980 are entirely spurious, and those of HD 50773 to a large extent. In the former case, this is shown to be due to the neglect of a strong magnetic field, and in the latter case, due to noisy spectra in combination with considerable rotational broadening and ensuing strong line blending. Doppler maps for other magnetic ApBp stars could be affected by similar problems. It is also pointed out that the patchy, extreme overabundances in HD 3980 cannot be reconciled with the theory of stellar atmospheres.