Quato's iColor Display 3 software has inbuilt generic corrections for W-LED and wide gamut backlighting units when using the software with some colorimeters. apart from with their own range of screens where the corrections are quite specific, they are generic though so you may find it doesnt actually help much when the white point is only 100 - 300k out in the first place. That "correction" may be altering the white point even more than is needed so it may just skew it in the other direction or too much. Remember, by white point i only mean the colour temperature and im sure if you calibrated with a target of 6500k, you wouldnt notice any issues in normal use anyway, even in in reality it was slightly cooler or warmer (and it's normally a little warmer, probably will be ~6200 - 6400k in reality).
and no, ive not tested the ColorMunki myself yet