The anomalously low ortho-to-para ratios (OPRs) exhibited by gaseous water in space have been used to determine the formation temperature (<50 kelvin) of ice on cold interstellar dust. This approach assumes that the OPR of water desorbed from ice is related to the ice formation temperature on the dust. However, we report that water desorbed from ice at 10 kelvin shows a statistical high-temperature OPR of 3, even when the ice is produced in situ by hydrogenation of O₂, a known formation process of interstellar water. This invalidates the assumed relation between OPR and temperature. The necessary reinterpretation of the low OPRs will help elucidate the chemical history of interstellar water from molecular clouds and processes in the early solar system, including comet formation.