This is a common misconception. Instead of using soil as a growing medium we use water. Water gives us a more uniform root environment for the plants in terms of uptake of water and nutrients. All vegetable farms have to supply fertilizers to ensure adequate nutrient levels to enable plant growth. The nutrients are supplied either as an inorganic (i.e. man-made) fertilizer or as an organic fertilizer. However the plant only uptakes nutrients in the form of ions which are either positive or negative charged. These final forms of nutrient ions are the same whether they are supplied from an organic or an inorganic fertilizer.
We use a recipe of both organic and inorganic fertilizers - (therefore we cannot be classified as organic). All cultural operations above water are identical to that used by growers in soil. We choose to have a minimum usage of both natural derived and man-made pesticides (again we cannot be classified as organic). In other words by growing in hydroponics or aeroponics does not mean that the production is automatically organic.