Molecular dynamic modeling of the nonlocal dielectric response of liquid water predicts a so-called "overscreening effect" which means an oscillating behavior of the electrostatic potential around the charged species. Calculations of the ion solvation energy for such a medium within the framework of the Born model of the ion charge distribution (its localization on the external surface of the ion cavity) result in values strongly exceeding even the solvation energy for the local-dielectric model of the surrounding medium, which is known as overestimating the experimental data for alkali ions. In this context it was a surprising result [J. Chem. Phys., 1996, 104, 1524] that a sufficiently broad distribution of the ion charge along the radial coordinate might lead to a strong diminution of the predicted solvation energies, up to their proximity to experimental values. Our actual study has been carried out to uncover the physical origin of this enormous reduction of the solvation energy for this model which combines the overscreening effect in the solvent response and a smeared out distribution of the ion charge. It has demonstrated that the shift of the charge density of the ion from the cavity's surface inside the cavity (in particular, with its smearing out along the radial coordinate) may only result in a further increase of the solvation energy. It means that a strong reduction of its predicted values allowing one to achieve their proximity to experimental data for alkali ions can only be achieved owing to the ion charge spreading out of the cavity, with its penetration into the solvent.