The OH-stretch induced dynamics in fluorosulfonic acid (HSO3F) is characterized from a statistically significant number of trajectories using multisurface adiabatic reactive molecular dynamics (MS-ARMD) simulations. The global reactive potential energy surface, which describes H-transfer and HF-elimination, is parametrized at the MP2/6-311G++(2p,2d) level of theory with an accuracy of better than 1 kcal/mol. Excitation along the OH-local mode leads to H-transfer dynamics but elimination of HF is only observed for excitations with nu >= 6 for 1 out of 5000 trajectories. This finding differs fundamentally from the situation for vibrationally induced photodissociation of H2SO4 and HSO3Cl, for which, even with excitations of 4 quanta along the OH-stretch mode, elimination of H2O and HCl, respectively, is readily observed on the subnanosecond time scale. RRKM rates for HX-elimination in HSO3X (X = F, Cl) only differ by a factor of 5. The findings from the reactive molecular dynamics with the RRKM results thus indicate that the origin for a closed HF-production channel is dynamical. This is also consistent with experimental findings for hydrofluoroethanes in shock tubes, which found pronounced non-RRKM behavior.