Probably, your characterization department has trouble making good measurements in such a low-current region, or they may not have even looked at data in that region.  I would expect it to be more strongly dependent on the accuracy/effort put into the extraction, rather than the model equations (BSIM4 vs PSP), though one might find that the more physical PSP model naturally gives you a consistent and accurate result for low VGS, whereas BSIM4 would need some further empirical parameter adjustments.