The H + HD → HD(ν′, j′) + H reaction has been studied experimentally and theoretically. Differential cross sections of HD(ν′, j′) products have been measured by means of a Photoloc technique and calculated using a time-independent quantum mechanical theory. Three product states: HD(ν′ = 1, j′ = 8) at a collision energy (Ecoll) of 1.97 eV; HD(ν′ = 2, j′ = 3) at Ecoll = 1.46 eV; and HD(ν′ = 2, j′ = 5) at Ecoll = 1.44 eV, show very good agreement between theory and experiment. The other two, highly rotationally excited states studied, HD(ν′ = 1, j′ = 12) and HD(ν′ = 1, j′ = 13) at Ecoll = 1.97 eV, exhibit a noticeable disagreement between experiment and theory. This is consistent with our most recent findings on the H + D2 → HD(ν′, j′) + D reaction, wherein the differential cross sections of HD(ν′ = 1, high j′) product states showed similar disagreement between the experiment and theory [J. Jankunas, M. Sneha, R. N. Zare, F. Bouakline, and S. C. Althorpe, J. Chem. Phys. 138 (2013) 094310]. In all five cases, however, we find overwhelming support that the experimental signal is a sum of reactive and inelastic scattering events. The interference term escapes detection, frustrating our attempt to observe geometric phase effects. Nevertheless, this work constitutes a first experimental example in which the indistinguishability of reactive and inelastic channels must be taken into account explicitly when constructing differential cross sections.