You have a misunderstanding of colours.
White doesn't really exist, but it is defined as (non-specular) reflection of standard illumination (ISO standard about paper say nearly 90% of reflection).
So white depends on brightness, so with the same light, you can see black, grey, white, or super-white. Just out eyes adapt quickly to a reference white.
For emissive devices, this is more tricky because emission doesn't depend on ambient light. For this reason, since years we have some sort of ambient light detection, so that software can tell screen to reduce brightness (or/and to change white balance [in this case "white balance" is about colours, not brightness).
If one person dim the screen, probably it is because it has less ambient light, and such person is not seeing white correctly. In any case, the eyes (and brain) will adapt quickly.
In short: white is a uniform colour at maximum brightness. if you dim the screen, it will appear grey for a short amount of time, because we had a different idea of maximum brightness. but we adapt.
Note: we have two adaptation: brightness and colours. Good filmakers may use it for good, but also colourists must handle it (on long grey scenes, not to make us to adapt and see it white).
Note: hardware may have two kind of brightness: one, the classic done by RGB, and one about global brightness (the backlight, also if now there is not more backlight). If you save screenshot, it takes just the RGB, and not the corrected values. But also if you take a photo, every cameras check the brightness, and automatically expose the photo (the average brightness of an image should be rendered as mid-grey). So also in this case you see no differences (if you really want to see it, you should set your camera in manual exposition mode, and take the two photos with same setting).
