The effect of van der Waals dispersion correction in combination with density functional theory is investigated on a canonical amorphous phase-change material. Density functional theory (DFT), using the generalized gradient approximation, usually fails to reproduce the structure of amorphous tellurides, which manifests by an overestimation of the interatomic bond distances, and particularly the Ge-Te one involved in local geometries (tetrahedral or defect octahedral). Here, we take into account dispersion forces in a semiempirical way and apply such DFT simulations to amorphous GeTe. We obtain a substantial improvement of the simulated structure factor and pair-correlation function, which now reproduce the experimental counterparts with an unprecedented accuracy, including on a recent partial contribution from anomalous x-ray scattering and from x-ray absorption. A detailed analysis of the corresponding structures indicates that the dispersion correction reduces the Ge-Te bond length, increases the fraction of tetrahedral germanium, and reduces the presence of heteropolar so-called fourfold ABAB rings. Given that these structural features have been stressed to be central for the understanding of the phase-change mechanism, the present results challenge our current understanding of the crystal to amorphous transformation at play.