While there may be truth to the principle that noise adds the illusion of detail, in this example I think you are misinterpreting what you are looking at.

If I remove all the noise in its lower part, it will not look natural (from my point of view)

This is mostly because no noise-reduction algorithm can perfectly remove all noise and retain all detail. The version you get after you run your noise-removal is not an accurate representation of the scene without any noise, but instead is an image that has been altered, removing some noise but along with it removing or altering detail as well.

Different algorithms vary in the final result, but nothing that removes a substantial amount of noise will give you something looking just as "natural" as the original had it not had noise. The variance between algorithms only alters how unnatural, and in what way it is unnatural.

A more appropriate experiment might be to start with an accurate, low-noise photograph and add noise to it.

As to the original claim, noise can at least mask some noticeable artifacts, and masking noticeable artifacts can give the illusion that you started off with a more faithfully accurate image in the first place. Noise can mask banding that you'd otherwise get from 24 bit colour in some gradients, it can mask blocking if the image used lossy compression, and it can mask unnatural smoothing/noise reduction (as in, if an image looks unnatural because of too much noise reduction, adding back in a little bit of noise can mask that and make it look "less unnatural"). That said, in none of these cases is it actually adding any accurate detail, it's just giving the illusion of a more faithful image because it's masking tell-tale signs of unfaithfulness.