We report on the photon energy dependence of the K-shell double photoionization (DPI) of Mg, Al, and Si. The DPI cross sections were derived from high-resolution measurements of x-ray spectra following the radiative decay of the K-shell double vacancy states. Our data evince the relative importance of the final-state electron-electron interaction to the DPI. By comparing the double-to-single K-shell photoionization cross-section ratios for neutral atoms with convergent close-coupling calculations for He-like ions, the effect of outer shell electrons on the K-shell DPI process is assessed. Universal scaling of the DPI cross sections with the effective nuclear charge for neutral atoms is revealed.