Chemistry of interstellar H2O is essential for understanding the formation of stars and planetary systems because of the ubiquity of H2O in space. The abundance ratio of nuclear spin isomers (the ortho-to-para ratio, OPR) can be a key for interstellar water chemistry, when assuming that the OPR desorbed from ice is closely related to the ice formation temperature. However, the above assumption has not been experimentally validated. Here, we report that H2O photodesorbed from ice at 10 K shows a statistical OPR of 3, even when the ice is produced in situ by hydrogenation of O2, a known formation process of interstellar H2O. This invalidates the hypothesis for relation between OPR and temperature. Reinterpretation of previous observations is necessary to improve our understanding of interstellar chemistry and the formation of the solar system and comets.