Molecular hydrogen is the third most abundant species in Titan's atmosphere with a tropospheric/lower stratospheric mole fraction of 0.001 derived from Voyager and Cassini measurements and the major species in Saturn's atmosphere. The motivation for this paper is to explore the hypothesis that the corrected H2 density measurements reported by Cassini Ion Neutral Mass Spectrometer (INMS) team were too high by a factor of 2.2, the factor that the INMS team reported in Teolis et al. (2015) as applicable to all species with no exceptions. For Titan, this would lead to the resolution of a possible missing H2 source and eliminate the need for a large downward gas phase H2 flux. For Saturn this would bring the INMS in-situ and UVIS stellar occultation H2 density measurements into agreement in the low latitude thermosphere and attribute the additional mass density derived from Cassini Attitude and Articulation Control Subsystem (AACS) exceeding the reduced INMS H2 mass density to infalling ring particles.