I personally believe this is a myth. I've yet to see a conclusive experiment that shows an airstone does not directly add oxygen to the water. I have seen conclusive studies that show that if you use a deep water air stone like are used for some tilapia recirculating raceways, you can get oxygen saturation. By deep water I mean 50 feet or more. The system is designed to provide the motive force to move the water through the biofilter and raceway. It has the added benefit of providing water that is oxygen saturated.

I also know that in my aquariums, simply agitating the surface with water flow from a filter is not nearly as effective as using an airstone for DO.