You most certainly can add cooled, de-oxygenated water at bottling time, I have done this several times with great success.
What I do is boil the water for 10 minutes the night before bottling and let it cool overnight. I add this to the bottling bucket, being careful not to splash. Then siphon the beer into the bottling bucket, add your primer, stir, and bottle.
Some breweries with limited space will make concentrated beers and will then dilute the final product.