Diapycnal turbulent mixing in the Southern Ocean is believed to play a role in setting the rate of the ocean Meridional Overturning Circulation (MOC), an important element of the global climate system. Whether this role is important, however, depends on the strength of this mixing, which remains poorly qualified on global scale. To address this question, a passive tracer was released upstream of the Drake Passage in 2009 as a part of the Diapycnal and Isopycnal Mixing Experiment in the Southern Ocean (DIMES). While the mixing rates inferred from vertical dispersion of the tracer are large and imply a key role played by mixing in setting the MOC, those based on localized microstructure measurements seem to suggest otherwise. In this work we use a high resolution numerical model of the Drake Passage region, sampled in the DIMES experiment and tuned to its observations, to explain that the difference between the two estimates arise from the large values of mixing encountered by the tracer when it flows close to the bottom topography. We conclude that enhanced bottom mixing, in combination with large lateral stirring and mixing by mesoscale eddies, is sufficiently strong to play an important role in setting the Southern Ocean branch of the MOC below 2 km.