I'm refering specifically to this question:
Not everyone can boil the needed full 5 gallons of water at a time.
Many times 2-3 gallons are brewed with the extract, cooled, and then the additional 2-3 gallons of water are added to bring the total volume to 5 gal.
The question to which you refer is asking if the additional 2-3 gallons also need to be sterilized through boiling.
You likely wouldn't be adding water to cooled wort, but many brewers add water to cooling wort for a number of reasons.
A brewer may not have a large enough kettle to brew the entire batch at once and must add additional water, or a brewer may add water to a wort to reduce its OG. However, in both of these scenario's the wort is more likely to be cooling rather than cooled. The only scenario that I can imagine is if for some reason you cannot correct for temperature when measuring OG and need the wort to cool before you can accurately measure it. Adding water to cooling wort can have a beneficial effect on the cooling if the water itself is cool, and I would regard it as a mistake if the wort had finished cooling by the time I realized that I needed to add more water for any reason.
I hope this isn't too pedantic a distinction.