Entities such as ion distributions and forces between lipid membranes depend on effects due to the intervening salt solution that have not been recognized previously. These specific ion or Hofmeister effects influence membrane fusion. A typical illustrative example is this: measurements of forces between double-chained cationic bilayers adsorbed onto molecularly smooth mica surfaces across different 0.6-2 mM salt solutions have revealed a large degree of ion specificity [Pashley et al. J. Phys. Chem. 1986, 90, 1637]. This has been interpreted in terms of very specific anion "binding" to the adsorbed bilayers, as it would too for micelles and other self-assembled systems. However, we show here that inclusion of nonelectrostatic (NES) or ionic dispersion potentials acting between ions and the two surfaces explains such "ion binding". The observed Hofmeister sequence for the calculated pressure without any direct ion binding is given correctly. This demonstrates the importance of a source of ion specificity that has been ignored. It is due to ionic physisorption caused by attractive NES ionic dispersion potentials. There appear to be some far reaching consequences for interpretations of membrane intermolecular interactions in salt solutions.