Dissolved oxygen is not the same as the oxygen in water molecule. Think of the fizz in soda. That comes from the dissolved carbon dioxide. You can have soda that is flat and that is very sharp. The same way you can have water with less dissolved oxygen or more.
In more technical terms, think of dissolved oxygen/carbon dioxide as gas molecules held in cage of water molecules. The more cages you make, the more you can dissolve these gases until you reach the maximum amount possible at a given temperature/pressure.