Molecular mechanics (MM) force fields employed in molecular dynamics simulations of bulk liquid water or of solvated proteins have to appropriately handle the sizable polarizability alpha of the water molecules. Using a hybrid method that combines density functional theory (DFT) for a rigid water molecule with an MM description of the liquid environment, we have recently shown that the induced dipole moment can be accurately calculated by linear response multiplying the experimental gas phase polarizability alpha(exp) with the electric reaction field averaged over the volume of the molecule [B. Schropp and P. Tavan, J. Phys. Chem. B 2008, 112, 6233]. However, water molecules are flexible, and the strong local fields acting in the liquid can change their geometries. These changes of geometry can modify both the dipole moment and the polarizability. Using a DFT/MM approach for a flexible DFT water model, here we show that the corresponding effects are quite small. Moreover, they even happen to cancel. As a result, rigid, transferable, and polarizable MM models automatically include the couplings between the external field in the bulk liquid, the geometry, and the dipole moment of an embedded water molecule.