Yes, greyscale impacts colors. You can think of it as the "exact color of paper" on which you then draw upon with colored pens. Of course the analogy falls apart even before the start, because RGB is an additive color system and therefore by definition there can be no "physical medium" equivalent.
If you are looking for a more factual explanation (
No clue what white does in greyscale settings (luminance? beamer specific?). Also calibrating greyscale AFTER youve applied a 3D LUT is a no go.
Also, I tried _many_ greyscale configurations until I hit those setting. I had other ones where greyscale was even more perfect (as you can see the RGB lines arent aligned perfectly), but they produced higher dE's in color checker.
BUT. You always have to keep the 6500K graph (white line) in mind. From my experience it is detrimental that it kisses the D65 line (at least from 30 IRE to possibly 100 IRE) and does not deviate in any direction (up/down), not even for about 100K (if your display is capable of such a configuration), because it will negatively impact color performance.
Or in short - I did "compensate" (measured again, and again, and again, ...) display characteristics with very specific greyscale settings, but NEVER to the point where the D65 graph would visibly suffer.
(f.e. on warm 2 (2pt greyscale) -1,-4,0;0,0,0(/-1) would deliver more accurate greyscale, but -2,-5,0;-1,-1,-2 more accurate color performance (with the greyscale dE's you see in the screengrabs I posted).
(btw. (might be useful to some) Irfanview (Freeware img editor) can be used to very easily create a "panorama image" of several screengrabs in a column (workflow is print(take screengrab)/ctrl+v into Irfanview/ctrl+H to original size/draw rectangle(mouse) and ctrl+Y to crop/S to save as -- once you've all individual screengrabs: image/create panorama)