Just to add to this... Here's what I think is going on with the minimum neutral feature with some numbers to back it up...
BCD profiles to the target white point. When it first starts profiling, I suspect they measure the native (and for clarity what I'm talking about has nothing to do with minimum native vs. minimum neutral, I think those are just unfortunate names for those features) color temperature of black. At some point, a weighted curve is applied. As you get closer and closer to black, the target color temperature starts going from the specified white point color temp, to the measured native black color temp.
Here's some measurements... in this case the target color temp was 6275. Here's measurements for achieved color temp from 255, 255, 255 to 0,0,0 (taken with Spectraview II and an i1Display Pro):
255 - 6275ºK
223 - 6250ºK
191 - 6275ºK
159 - 6254ºK
127 - 6275ºK
095 - 6235ºK
063 - 6235ºK
031 - 6415ºK
023 - 6865ºK
015 - 8225ºK
011 - 9355ºK
009 - 10200ºK
007 - 11050ºK
005 - 12400ºK
003 - 13600ºK
001 - 15300ºK
000 - 15530ºK
So it would appear as if the numbers support this theory and with that I think that minimum neutral corrects chroma for whatever the target white point happens to be along that weighted curve and minimum native simply doesn't bother to correct for chroma (or more accurately a curve defines how much chroma correction is applied, and chroma correction is eventually eliminated altogether), it just makes sure that the luminance is where it should be at.
The reason they gave for that particular feature is because as we know, Spectrophotometers lose accuracy as the signal to noise ratio decreases as you get closer to black. The option of minimum native relies upon the linearity of the monitor as you get closer to black and forgoes the attempt to correct chroma. Given the error that pucks like the ColorMunki Photo are prone to in the shadows, using minimum native can reduce color casts in the shadows that are the result of sensor noise.
I believe the source of my own confusion on this particular feature reside with what in my opinion is a very unfortunate name. I'm willing to bet that the German localized version makes a lot more sense as the product is developed in German (any Germans here that can verify this?) but as an English speaker the term "neutral" to me is the literal definition in the dictionary which is "a neutral color or shade". In this case "neutral" is defined by the white point target. A profile that gets increasingly blue as you get closer to black is not what I would describe as being "neutral", hence my confusion. When I saw the word "neutral", I expected that feature to behave in the same manner as SpectraView II's "optimize for greyscale" option in the calibration priority preferences.
Cheers, Joe