We analyze the production cross sections and isotopic distributions of projectilelike residues in the reactions Sn112+Sn112 and Sn124+Sn124 at an incident beam energy of 1 GeV/nucleon measured with the fragment separator at the GSI laboratory. Calculations within the statistical multifragmentation model for an ensemble of excited sources were performed with ensemble parameters determined previously for similar reactions at 600 MeV/nucleon. The obtained good agreement with the experiment establishes the universal properties of the excited spectator systems produced during the dynamical stage of the reaction. It is furthermore confirmed that a significant reduction of the symmetry-energy term at the freeze-out stage of reduced density and high temperature is necessary to reproduce the experimental isotope distributions. A trend of decreasing symmetry energy for large neutron-rich fragments of low excitation energy is interpreted as a nuclear-structure effect.