What it means Shortymet is that if you have good water circulation, not just at one level, then you don't need an air pump. The other half of the equation, as Rabbut said, is that the water must move vertically in the tank and mix properly. If your filter isn't giving you the good vertical as well as horizontal mixing, you will need something that does. One of the easiest ways to get it, if the filter doesn't do it, is an air stone. The water that is near the bottom of the tank must somehow be brought to the surface to absorb oxygen so you need to provide good circulation to do that.
Edit to add info:
BTW Rabbut and I do not disagree on anything but our observations. He has seen poor vertical circulation from filters, but in my tanks I am seeing good vertical circulation from my filters. We definitely agree that circulating water vertically is essential to good aeration.