We have performed X-ray specular and off-specular measurements of free-standing polystyrene thin films as a function of molecular weight and thickness. The results show films thicker than a few radii of gyration (Rg) are well fit by a simple liquid model. This confirms the assumption that the anomalies previously reported in the scattering intensity from polymer films of comparable thickness were mostly due to confinement by long-ranged interactions with the substrate rather than a fundamental property of viscoelastic fluids. The simple liquid model was found to be insufficient to fit the transverse diffuse data for films thinner than a few Rg. Longitudinal diffuse scattering data demonstrated that the roughness at the two interfaces is highly correlated when the film thicknesses are approximately 2Rg. Hence, very thin films do not exhibit liquidlike behavior, and higher-order elastic terms may have to be included into models to describe their rheological behavior.