Trans Fluid to Use?

We have a member here who wrote a book on the 727 and is pretty knowledgable on it. He recently rebuilt my transmission using all the good parts that he had stashed around his basement. When I eagerly asked him what fluid I should run, he told me to go get a case of the cheapest Dexron III that Wally World has. This is for a street car that we beat on pretty hard. When I questioned him about buying some fancy expensive fluid, he simply said it wasn't needed.