I'm not sure why they're jumping on your case. You're right.
Light can absolutely affect the quality of an image, because light reacts uniquely with unique materials. A texture map can look completely different (flat vs textured) in different light. That's why lighting, in games as well as film, is considering an art.
It is possible for very few shadows to appear on the surface of an object when viewed (or lit) from one angle vs another. Maybe when textures were "only" flat (I mean, I guess they still are) it didn't matter, but now I think it does, since shaders and other tech allow for accurate material simulation.
Now, the actual geometry or assets? Time of day probably doesn't affect those as much, I agree.
Weather can impact it, simply because it can completely change the screen color temperature--and of course, cloudy lighting will have completely different characteristics than direct, hard sunlight.
I mean, what we actually need is an accurate technical comparison, and why wouldn't you want there be as few variables present, outside of the actual devices/platforms?