The dynamics of water molecules next to hydrophobic solutes is investigated, specifically addressing the recent controversy raised by the first time-resolved observations, which concluded that some water molecules are immobilized by hydrophobic groups, in strong contrast to previous NMR conclusions. Through molecular dynamics simulations and an analytic jump reorientation model, we identify the water reorientation mechanism next to a hydrophobic solute and provide evidence that no water molecules are immobilized by hydrophobic solutes. Their moderate rotational slowdown compared to bulk water (e.g., by a factor of less than 2 at low solute concentration) is mainly due to slower hydrogen-bond exchange. The slowdown is quantitatively described by a solute excluded volume effect at the transition state for the key hydrogen-bond exchange in the reorientation mechanism. We show that this picture is consistent with both ultrafast anisotropy and NMR experimental results and that the transition state excluded volume theory yields quantitative predictions of the rotational slowdown for diverse hydrophobic solutes of varying size over a wide concentration range. We also explain why hydrophobic groups slow water reorientation less than do some hydrophilic groups.