The currently most precise measurements of the top quark mass are obtained from kinematic reconstruction obtained at hadron colliders. The observables designed to make these measurements cannot be calculated using analytic methods in QCD and therefore reply on multipurpose Monte-Carlo event generators. As a consequence, the interpretation of the measured top quark masses is theoretically difficult. In my talk I explain the theoretical issues inherent to this problem. It is currently also not yet fully understood, up to a conceptual upper bound, how large the uncertainty is when one interprets the result as measurements of the pole mass. I then explain one approach to shed some light on the interpretation problem using the concept of MC calibration with top mass sensitive observables which can be computed systematically at hadron level using analytic methods. As these observables can currently only be calculated for boosted top quarks, the problem of how the current most precise top quark mass measurements have to be interpreted is strictly speaking still open.