However, we have heard from them that they purposely include some saturation change consistently with contrast change because their research demonstrates that most people would not find the result of a pure luminosity change of contrast to look "natural".
The true is that a change in exposure, i.e. a linear scaling of the RGB values that can for example be achieved with a curve passing by (0,0) as described, is the only possible pure luminosity change.
Anything else: HSB/HSV colour models, Lab, blending modes, etc... are just perceptual models to help us deal with the concepts of luminosity and colour (typically split in these models into hue and saturation, or the ab channels, etc...). E.g. if you push L a lot in Lab mode, the proportions between R, G anB will change to finally end in pure white. Speaking in physical terms, that is not only pushing luminosity but also desaturating, i.e. changing colour. Changing the luminosity of a red lamp consists of producing more red light, not turn the red lamp into a pink lamp and finally white.
So paradoxically, changing luminosity using those tools or modes typically intended to allow a control of luminosity without altering colour, means changing not only luminosity but also colour (of course in a way perceptually as pleasant and natural as possible).