Toolish,
You'll find that there are quite a few RT phrases the are specific to Australia and not ICAO standard, much like there are all over the world. (I'm not going to use the words "pedantic" and "Australia", in the same sentence, though).
The Delta guys, as well as United and American won't be aware of them. Although, "Charlie, Charlie" is not a term I've ever heard in the US or anywhere else, it may be more of a US military term as they tend to have more former military guys among their ranks.