Acceptor-doped barium zirconates are currently receiving considerable interest because of their high proton conductivity at intermediate temperatures, making them applicable as electrolytes in various electrochemical devices, but the mechanism of proton conduction is unclear. Here, we investigate the role of the acceptor-dopant level in the localized proton motions, i.e. proton transfers between oxygens and O-H reorientations, in hydrated samples of the proton conducting, acceptor-doped, perovskites BaZr1-xInxO3-x/2 with x = 0.10 and 0.20, using quasielastic neutron scattering (QENS). Analysis of the QENS spectra reveals that several proton transfer and O-H reorientational motions contribute to the QENS signal, as a consequence of the locally disordered nature of the structure due to the In doping of these materials, and establishes a generic and complex picture of localized proton dynamics in acceptor-doped barium zirconate based proton conductors. A comparison of the QENS results with vibrational spectroscopy data of the same materials, as reported in the literature, suggests a predominance of O-H reorientational motions in the observed dynamics. The highest doping level corresponds to a more distorted structure and faster dynamics, which thus indicates that some degree of structural disorder is favourable for high local proton mobility.