Brillouin microscopy measures compressibility, but is being increasingly used to assess stiffness of cells and tissues. Using hydrogels with tunable properties, we demonstrate that Brillouin microscopy is insensitive to stiffness of hydrated materials, but depends strongly on water content, consistent with a theoretical model of biphasic compressibility. Empirical correlations between Brillouin measurements and stiffness arise due to their mutual dependence on water content, but correlations vanish once hydration is controlled.