A quasi-chemical (QC) model of one-component fluids is considered that circumvents limitations of traditional QC treatments by incorporating "boundary" interactions-those interactions that involve molecules both external and internal to the fundamental cells or subvolumes inherent in QC fluid theories. This is achieved by including correlations between the energy and density of the subcells and the surrounding fluid, based on a representation of configurational probabilities within the small system grand canonical ensemble, and motivated in part by the behavior of such correlations observed in molecular simulations of a simple body-centered cubic lattice gas with nearest-neighbor attractions (bcc-LG). Energy and density correlations are included at an athermal level in the present work. The resulting model is found to give significantly improved predictions of the effects of temperature on local density fluctuations compared to the case in which such correlations are neglected, with results in semi quantitative agreement with those from molecular simulations. Despite only semi-quantitative agreement at the level of subvolume density fluctuations versus temperature, the resulting equation of state (EoS) is dramatically improved over traditional treatments in which boundary interactions are neglected. The QC EoS with boundary interactions gives predictions in excellent agreement with simulated bcc-LG vapor-liquid phase boundaries at T/T-c < 0.82. As expected due to the limited subcell dimensions, predictions are in poorer agreement as T-c is approached. In contrast, the QC model without boundary interactions predicts no phase separation at positive temperatures.