The difference is here between input and output.
You tell the module “I want the output to be gray”. The implies that in the output, the values for red green and blue must be the same, and it’s that output that is represented in the histogram.
Now, on the input side, you can vary the relative weights of red, green, and blue. The module will take care of the translation of colour into gray tones based on those relative weight of the three channels, and the colour of the pixel.
To pick up your blue sky example: what happens if you push the blue input slider to a very low value (and increase red and green to make life easy on the module)?
And do check out @anon41087856’s use of the brightness tab in the thread presenting this module (the two photos of a sunset, where he increases the red brightness and lowers the blue).
It’s normal to see all colours affected in both brightness and gray mode: the colour spaces we use have three dimensions/axes. either red|green|blue or brightness|coloration1|coloration2.
It’s important to keep in mind that those are different representations of the same underlying data. As such, transformations between them are a simple mathematical operation.
Grayscale is a special case where you force extra relations between the dimensions, leaving you with variations possible in only one of the dimensions.
In both gray and brightness mode, you do not want to change the two coloration dimensions (chroma|saturation, a|b, hue|saturation, however you want to call them) for your output. Thus, any change in one input colour channel must lead to a change in all three colour channels in the output (which is what the histogram shows).(*)
But for an individual pixel, the change in the output will depend on how much of the colour channel you changed is in that pixel’s original colour. E.g. 10% red → only 10% of the change for the red channel will be applied.
(* : A 2D example could be the relation between Carthesians coordinates (x,y) vs polar coordinates (r,φ),
when you change xn keeping y constant, both r and φ will change. Vice versa, change either r, (or φ,) and both x and y will change.)