This work comprises the thermodynamic characterization of hydrophobic-water solutions using a recently introduced Hamiltonian of liquid water, which reproduces the short-ranged oxygen order while permitting all hydrogen bonding interactions to be isotropic. The thermodynamics of methane association is evaluated with this isotropic potential and compared to free energy simulations of methane-like groups in well-established models of liquid water where full anisotropy of hydrogen bonding is described. We find that the isotropic fluid reproduces the trends in free energy as a function of solute-water parameters, and that the free energy profiles appear to be quantitatively robust. The thermodynamic breakdown of the free energy indicates that the roles of entropy and enthalpy are reversed for quite small changes in the Lennard-Jones methane-solvent length parameter, sigma, implying that molecular pictures of hydrophobic hydration based on reducing the exposed hydrophobic surface may be incomplete. This new Hamiltonian offers significant computational advantages and improved convergence of the thermodynamic Components of the free energy when compared to the anisotropic water models. Furthermore, it offers a straightforward means for characterizing water as a solvent at different values of temperature and pressure.