There's a difference between "prototypical objects" and "specific objects". For instance, apples are red, but that specific apple you have in your hand might be green. Likewise, people have 10 fingers, but my grandmother only has 9. I suspect the parent thought this distinction was hidden in the question?
But I don't see any reason you couldn't name a specific object in response to the "everything in the world" question. I also can't think of many objects that are white but not prototypically white. So maybe I've misunderstood too.
To give an example of this... When answering the first question, I found myself thinking only of things which are pure white almost all the time. So I thought of snow, clouds, white sails - and even with those I felt they were arguable (snow can be grey; clouds too; sails can be multi-coloured). Arguably the only thing that's prototypically white in the world is sunlight - and that looks yellow! :-P
On the other hand, when considering my fridge, I only thought of what is white-looking in there... Milk is prototypically white, but cheese, eggs, bread, mold on some old sausages, etc... are just kinda sorta white sometimes. But within the limits of a fridge they're acceptable examples of white.
I think that's what the GP was arguing: when asked for "white things in the world" you naturally place the bar for "white" much higher than when asked for "white things in your fridge".
But I don't see any reason you couldn't name a specific object in response to the "everything in the world" question. I also can't think of many objects that are white but not prototypically white. So maybe I've misunderstood too.