I have to say that my interest in photographic matters leans strongly towards the practical application of the theory, which is why I frequently carry out my own tests on my own equipment, not necessarilly to prove or disprove the theoretical claims that are being made, but to find out how significant such claims for particular technical qualities may be in practice, and in what circumstances they may be of some advantage to my efforts in producing an image or print to my own satisfaction.
However, in order to make such tests one really has to understand clearly what it is one is testing, and therefore a precise definition of the fundamental concepts related to the features one is testing, is necessary.
I remember well the occasion when this phenomenon of improved image quality resulting from the use of an increased ISO first came to my attention. It was on the old Rob Galbraith photographic forum around the year 2005/6. A poster by the name of John Sheehy made a comment to the effect, "It is better to use an exposure at ISO 200 than ISO 100 because you get better shadow detail."
Now, being the sort of guy who refuses to accept anything that doesn't make sense, I chimed in and disputed his claim. How can an exposure at ISO 200 possibly be better than an exposure at ISO 100? At ISO 100 the sensor receives double the amount of light. SNR is bound to be better.
John quickly dispelled my confusion by explaining that he was referring to circumstances where the same exposure was used at both ISO settings. My misunderstanding was due to my conflating ISO settings with actual exposure, which is quite understandable because we always have to either deliberately choose a specific ISO everytime we take a shot, or allow the camera to automatically choose it for us.
In order to avoid such confusion, I think it is better to consider exposure as something which is determined only by F/stop, shutter speed, and that quality we often ignore, T/stop, which relates to the transmissive qualities of the glass in the lens.
The ISO setting is merely an instruction to the camera's internal processing electronics to process an exposure in a particular way.