The ortho-to-para ratio (OPR) of water in the interstellar medium (ISM) is often assumed to be related to the formation temperature of water molecules, making it a potentially interesting tracer of the thermal history of interstellar gas. A very low OPR of 0.1-0.5 was previously reported in the Orion Bar photon-dominated region (PDR), based on observations of two optically thin H_2_^18^O lines which were analyzed by using a single-slab large velocity gradient (LVG) model. The corresponding spin temperature does not coincide with the kinetic temperature of the molecular gas in this UV-illuminated region. This was interpreted as an indication of water molecules being formed on cold icy grains which were subsequently released by UV photodesorption. A more complete set of water observations in the Orion Bar, including seven H_2_^16^O lines and one H_2_^18^O line, carried out using Herschel/HIFI instrument, was reanalyzed using the Meudon PDR code to derive gas-phase water abundance and the OPR. The model takes into account the steep density and temperature gradients present in the region. The model line intensities are in good agreement with the observations assuming that water molecules formed with an OPR corresponding to thermal equilibrium conditions at the local kinetic temperature of the gas and when solely considering gas-phase chemistry and water gas-grain exchanges through adsorption and desorption. Gas-phase water is predicted to arise from a region deep into the cloud, corresponding to a visual extinction of A_V_~9, with a H_2_^16^O fractional abundance of ~2x10^-7^ and column density of (1.4+/-0.8)x10^15^cm^-2^ for a total cloud depth of A_V_=15. A line-of-sight average OPR of 2.8+/-0.2 is derived. The observational data are consistent with a nuclear spin isomer repartition corresponding to the thermal equilibrium at a temperature of 36+/-2K, much higher than the spin temperature previously reported for this region and close to the gas kinetic temperature in the water-emitting gas.