The cumulative reaction probability (CRP) has been calculated for the H-2 + OH <-> H2O + H in its full dimensionality by using the centrifugal sudden (CS) approximation for J > 0, The Boltzmann average of the CRP provides the most accurate thermal rate constant to date for the title reaction on the Walch, Dunning, Schatz, Elgersma (WDSE) potential energy surface (PES). It is found that the theoretical rate is larger than the experimental value in the low temperature region (a factor of similar to 1.8 at 300 K), and smaller than the experimental value for temperatures higher than 500 K, indicating that a more accurate PES is needed to provide a quantitative description of the title reaction, We also demonstrate that the "J-shifting" approximation in which we calculate N(J > K, K) from N(J = K, K) by an energy shift works very well for this reaction. However, the "J- and K-shifting" approximation [calculating N(J, K) from N(J = 0, K= 0)] overestimates the rate for this reaction by about 60% for all the temperatures investigated. It is also found that the CS rate constant is substantially lower than the rate constant for the ground rovibrational state of the reagents calculated on the same PES, indicating that initial rotational excitation is important to the thermal rate constant for this reaction (it causes a decrease).