Surface forces have been measured by others in undersaturated vapors to determine the adhesive energy of the solid (mica) as well as to probe the limits of the Laplace-Kelvin equation in micropores. The measured pull-off forces are complex requiring an intimate understanding of the underlying oscillatory solvation forces, adsorption, and surface deformation. While the elastic energy of the solid has been taken into account in previous theoretical studies of adhesion, the Laplace-Kelvin assumption of a uniform bulk-like fluid has always been applied. In this paper we present the first application of a modern molecular theory-a nonlocal density functional theory-to the prediction of pull-off forces with the surface forces apparatus. In this theory, the confined fluid is allowed to be nonuniform, and oscillatory solvation forces may be predicted. For rigid surfaces, it is demonstrated that the separation of forces most often used to analyze the surface forces apparatus measurements is highly accurate only when adsorption is properly treated and when the relative pressure is p/p(0)>0.2-0.4. The limiting value of the relative pressure decreases as the strength of the fluid-surface interaction increases. In addition, the range over which the vacuum limit of the solid surface free energy, gamma(s) may be measured is strongly dependent on the strength of various molecular interactions. We predict, as observed in experiments, that the saturation limit of the pull-off force is given by the Laplace pressure alone if there are at least two fluid layers between the surfaces. Finally, we show that using pull-off forces to test the limits of the Laplace-Kelvin theory is misleading because the measurements by design minimize solid-liquid contributions to the total force.