Many, including myself notice that Hydrogen Peroxide is nothing more than pure water with an extra oxygen atom attached to it.
As oxygen combines with the iron in steel, it will create iron oxide, commonly known as rust.
The "hydrogen peroxide" bought in a store is a very weak form of the stuff, many have noticed that it doesn't seem to rust their bores but as a pint of it can cost over $2.00 and I can buy a gallon of distilled water for 99¢ I don't see why anyone would want to spend the extra money.
IMO, the distilled water will clean black powder fouling just as well.