RGB curves - Why does adjusting the G curve also result in a change in R and B channels?

[sovereign (Matteo Costa)]

Hello @ggbutcher, thanks a lot for the detailed post.
To me the general approch is quite clear now.

What I still don’t get is the reason why the choice of the output profile should impact the rendering on screen. From the color management section in Raw Pedia:

Output Profile

Specify the output color profile; the saved image will be transformed into this color space and the profile will be embedded in the metadata. The effects the output profile has on the image cannot be seen in the preview.

The G & B channels are left untouched when R is modified only if the working profile matches the output profile:

sRGB —> RT_sRGB
Adobe RGB —> RT_Medium
ProPhoto —> RT_Large

Based on what I quoted above this should not happen.
What is it that I am missing here ?

NOTE: this time I am sure not to have enabled “fancy” features (like CIECAM02) or having misclicked somewhere (… luminosity mode in RGB curves module is OFF).