I thought there was a difference where self taught would be "I did teach myself this thing" and autodidactic would be "I have the personality trait of continually teaching myself new things." Only one of the dictionaries I checked made this fine grained (and relevant) distinction explicit though.
Simply saying "self-taught" wouldn't have had the right connotation: instead of "clever and driven", it would have been, "but what have they missed?" and we would have missed out on this interesting off-topic sub-thread!