Most experimental claims of Majorana bound states rest on the observation of a persistent zero bias peak (ZBP) in tunneling spectra.  In our paper, we provide comprehensive evidence that the ZBPs observed in the experiments with semiconductor nanowires fully coated with a superconducting shell are not of Majorana origin. Instead, our theory  demonstrates that ZBPs can be explained in terms of Yu-Shiba-Rusinov states (a special type of Andreev bound state) that originate in the tunneling region owing to the competition between electron correlations and superconductivity.