The diffusion of fluorescently labeled lipids in supported bilayers is studied using two different methods: Z-scan fluorescence correlation spectroscopy (z-scan FCS) and two-focus fluorescence correlation spectroscopy (2f-FCS). It is found that the data can be fitted consistently only when taking into account partial sticking of the labeled lipids to the supporting glass surface. A kinetic reaction-diffusion model is developed and applied to the data. We find a very slow sticking rate which, however, when neglected, leads to strongly varying estimates of the free diffusion coefficient. The study reveals a strong sensitivity of FCS on even slight binding/unbinding kinetics of the labeled molecules, which has significance for related diffusion measurements in cellular lipid membranes.