I have seen articles about this as well, and if it is set up properly, then it seems to be a viable way to raise your own fish for food, as well as grow your own vegetables, and each one helps the other to be healthy and grow better.
I have also read about a man that raised catfish in a 55 gallon barrel. He did not filter it onto a hydroponic garden, but he did reuse the water into his vegetable garden through a regular hose.
Then he also grew earthworms with the compost from the garden, and fed the works to the catfish, so it all worked together for him ,too.
He had to drain water from the bottom of the Barrell every day or so, and refill it with fresh water so the fish could breathe.