We have measured a negative thermal expansion (NTE) of the Co subnetwork in amorphous Nd1-xCox (0.78 < x < 0.84) thin films of the order of 1% in volume using linearly polarized EXAFS spectroscopy at RT and 10 K. The expansion, which is anisotropic, is uncorrelated with the perpendicular magnetic anisotropy (PMA) observed in all the films, but correlated with the method used to deposit them. The atomic environments of the Nd atoms resulted in such a strong disorder that Nd-Nd and Nd-Co environments were invisible to EXAFS, and only Co-Co atomic environments were detected. The information on the Nd subnetwork was obtained through its magnetic moment measured by XMCD. These measurements demonstrate an increasing interaction of neodymium atoms with their particular local crystal field as the temperature decreased, suggesting possible structural modifications at their sites. Since the magnetic moment of the cobalt subnetwork remains essentially constant with the temperature, it is proposed that its detected NTE may be caused by the mechanical response of the amorphous network to structural transformations at the Nd sites. These results support that the PMA in RE-TM alloys is localized at the RE sites. The complete absence of EXAFS oscillations in the Nd L3 EXAFS spectra is remarkable: it means that the coherence length of the photoemitted electrons in disordered matter can be strongly reduced from that expected by atomic calculations to the point of being less than first neighbor distances, which is contrary to the common belief that first neighbors are always visible by EXAFS.