The adhesion of lipid vesicles to solid supports represents an important step in the molecular self-assembly of model membrane platforms. A wide range of experimental parameters are involved in controlling this process, including substrate material and topology, lipid composition, vesicle size, solution pH, ionic strength, and osmotic pressure. At present, it is not well understood how the magnitude and direction of the osmotic pressure exerted on a vesicle influence the corresponding adsorption kinetics. In this work, using quartz crystal microbalance with dissipation (QCM-D) monitoring, we have experimentally studied the role of osmotic pressure in the adsorption of zwitterionic vesicles onto silicon oxide. The osmotic pressure was induced by changing the ionic strength of the solvent across an appreciably wider range (from 25 to 1000 mM NaCl outside of the vesicle, and 125 mM NaCl inside of the vesicle, unless otherwise noted) compared to that used in earlier works. Our key finding is demonstration that, by changing osmotic pressure, all three generic types of the kinetics of vesicle adsorption and rupture can be observed in one system, including (i) adsorption of intact vesicles, (ii) adsorption and rupture after reaching a critical vesicle coverage, and (iii) rupture just after adsorption. Furthermore, theoretical analysis of pressure-induced deformation of adsorbed vesicles and a DLVO-type analysis of the vesicle-substrate interaction qualitatively support our observations. Taken together, the findings in this work demonstrate that osmotic pressure can either promote or impede the rupture of adsorbed vesicles on silicon oxide, and offer experimental evidence to support adhesion energy-based models that describe the adsorption and spontaneous rupture of vesicles on solid supports.