We present an assessment of the probabilistic and climatological consistency of the CMIP5/PMIP3 ensemble simulations for the last millennium relative to proxy-based reconstructions under the paradigm of a statistically indistinguishable ensemble. We evaluate whether simulations and reconstructions are compatible realizations of the unknown past climate evolution. A lack of consistency is diagnosed in surface air temperature data for the Pacific, European and North Atlantic regions. On the other hand, indications are found that temperature signals partially agree in the western tropical Pacific, the subtropical North Pacific and the South Atlantic. Deviations from consistency may change between sub-periods, and they may include pronounced opposite biases in different sub-periods. These distributional inconsistencies originate mainly from differences in multi-centennial to millennial trends. Since the data uncertainties are only weakly constrained, the frequent over-dispersive distributional relations prevent the formal rejection of consistency of the simulation ensemble.