The representation of stable boundary layers (SBLs) still challenges turbulence parameterizations implemented in current weather or climate models. The present work assesses whether these model deficiencies reflect calibration choices or intrinsic limits in currently-used turbulence parameterization formulations and implementations. This question is addressed for the ARPEGE-Climat 6.3 CNRM atmospheric model in a single-column model/large-eddy simulation (SCM/LES) comparison framework, using the history matching with iterative refocusing statistical approach. The GABLS4 case, which samples a nocturnal strong SBL observed at Dome C, Antarctic Plateau, is used. The standard calibration of the ARPEGE-Climat 6.3 turbulence parameterization leads to a too deep SBL, a too high low-level jet and misses the nocturnal wind rotation. This behavior is found for low and high vertical resolution model configurations. The statistical tool then proves that these model deficiencies reflect a poor parameterization calibration rather than intrinsic limits of the parameterization formulation itself. In particular, the role of two lower bounds that were heuristically introduced during the parameterization implementation to increase mixing in the free troposphere and to avoid runaway cooling in snow- or ice-covered region is emphasized. The statistical tool identifies the space of the parameterization free parameters compatible with the LES reference, accounting for the various sources of uncertainty. This space is non-empty, thus proving that the ARPEGE-Climat 6.3 turbulence parameterization contains the required physics to capture the GABLS4 SBL. The SCM framework is also used to validate the statistical framework and a few guidelines for its use in parameterization development and calibration are discussed.