The lateral forces during stick-slip motion of an atomic force microscope cantilever on highly oriented pyrolytic graphite are measured and analyzed. We identify the regimes where thermally activated interstitial hopping of the cantilever tip proceeds according to a single-step reaction scheme and extract the corresponding force-dependent transition rates directly from the experimental data. We find that such a single-step reaction scenario is valid only at relatively high velocities, while at slower pulling speeds, a more complicated hopping mechanism must be at work. We suggest formation of multiple bonds of the tip-sample contact as a possible candidate for this mechanism.