the AHD, a real dictionary, might be wrong?

I think "wrong" might be a little strong. As wsieber said, "misleading" might be a little closer to the truth, although to suggest that AHD is saying it comes from the word for duke is probably a little misleading its own se'f. It merely refers us to the entry for duke to see more about the origin of dux. Merriam-Webster dates redux's entry into English to 1873. Might be intersting to see what OED has to say about the matter.