A hybrid of high level and low level quantum mechanics (QM) methods has been employed to predict intrinsic and apparent energy barriers for the direct proton exchange mechanism of methane, ethane, propane, n-butane, and i-butane on Brønsted sites of H-MFI. The specific hybrid MP2:PBE+D2 + ΔCC implementation used is known to yield the so-called "chemical accuracy" (±4 kJ/mol). Whereas the apparent enthalpy barriers decrease with increasing C number from 104 to 63 kJ/mol, in line with the decreasing heat of adsorption, the intrinsic enthalpy barriers are constant within 124-127 kJ/mol at 500 K. For methane, ethane, propane, and n-butane, we find the expected agreement of apparent barriers with activation energies from batch recirculation reactor experiments. The activation energies derived from NMR experiments (103-113 kJ/mol) are similarly constant as the predicted intrinsic barriers but systematically lower. For i-butane the predicted intrinsic and apparent barriers for the direct proton exchange step are the same as for n-butane with deviations of 2-5 kJ/mol, while the experiments yield values that are 50-60 kJ/mol lower, far outside the estimated range of combined experimental and computational uncertainty (±14 kJ/mol). A change to the indirect proton exchange mechanism, in which a hydride ion is transferred between the alkane and a tert-butyl carbenium ion can be excluded, because we confirm previous findings that the barrier for dehydrogenation that would create a tert-butyl cation from i-butane is much too high, 188 and 132 kJ/mol for the intrinsic and apparent enthalpy barriers, respectively, at 500 K. The possible role of extraframework- and framework-bound alumina species is discussed.