This is all subjective; it's not really a matter of "proof". You would find that your white paper will look very convincingly white when indoors, under all sorts of illumination (very yellow, dimmed filament lamps, for instance). That's because your colour vision is desperately trying to take out any perceived colouration due to to the illumination. Your brain tries to 'integrate to grey' - just like your digital camera also tries to do, and jiggles its colour channel gains accordingly. It can be very successful and it can also fail abysmally, when trying to match clothes colours in a shop, under artificial light. (Colour film is hopeless because it has only one setting for its colourimetry). That's why we take things out into the street to check.
The Sun is not particularly blue or particularly red/yellow, compared with all the other stars around there are much more extremes on other side of our 'white' Sun - intense blue stars that are burning up very quickly and are much hotter and some red giants that are cooling down at the end of their lives. Their particular colours of illuminant would be taken as normal (white?) by the local inhabitants.
Overall, coulorimetry is a fascinating subject, I think.