The question of whether silica nanoparticles can enhance the ionic conductivity of a polymer electrolyte above its crystallization temperature has remained unclear for the two decades following the first experiments on these systems. We use molecular dynamics simulations to decipher the atomic-scale mechanisms affecting the properties of LiTFSI-poly(ethylene oxide) electrolytes upon the addition of silica nanoparticles. At any ionic concentration, adding nanoparticles significantly decreases the conductivity. Most of this reduction can be simply accounted for by the diffusion equation, resulting from the fact that the space occupied by the nanoparticles is made inactive and unable to sustain ionic diffusion. We identify two distinct regimes, above and below a concentration threshold, corresponding to very different ionic distributions and coordination features of the various species. The lack of conductivity enhancement observed in the simulations supports the conclusions of some recent measurements and disagrees with the earliest experimental reports on hybrid silica/polyethylene-oxide electrolytes.