Encyclopedic knowledge ... oooookay.
No, a painted wall and a screen are not the same thing. And YES, the color of the wall absolutely matters. It matters a lot.
Grey is not a color. It is white (reflective) with black (absorbs). However, many grey screens are much more than that. It will reproduce colors exactly like a white screen.
Painted walls do one thing. They reflect. You can choose diffuse in which case you will get good uniformity, and imperfections in the wall will be hidden. If you go more glossy, your light level increases, imperfections are visible, and uniformity drops. One good point miller makes it the impact of light from the screen hitting things and bouncing back on the screen reducing contrast. Diffuse paint sends light everywhere, so more chance of it happening, but, when the light does go back to the screen, it creates a diffuse reflection. With a more glossy paint, if the reflection is away from you great, if not, not so great.
Purchased screen material can not only have gain (and you can buy many different gains), unlike paint, high end screens can also reject ambient light. They have surface structures designed so that light that enters from a larger angle does not reflect forward. That matters even if your room is completely dark as the light from the screen goes out into the room and comes back has a lower chance of then being reflected at the viewer. The result is better contrast.
wrt white paint and off-white, etc. No, you need a perfectly white paint if you want the best quality (or perfectly grey). If you have an off-white paint, yes, your eyes will adjust to "white" when they are presented with enough white on the screen, however, the balance between the colors will all be off so colors will not look right. It is akin to looking at objects with a warm white, or bright white light. You will perceive white as white, but the colors will look much different under the different lights.
