I don't think the Australians conceded anything.
Rugby League has been the dominant code there for several lifetimes and the fans there use the term League, Rugby League or Footy.
Rugby on its own was always considered the "toffs" version of the sport and Rugby League was never just called just "Rugby" by any Australians I know.
What are you going to do when we re-brand to call our sport "*********" and no other country follows with us?
The Aussies will not change their Sports name.
They look on the name "Super League" with derision because it sounds juvenile and is associated with the split in the game where the majority of the fans there did not like the Newscorp takeover.
We don't call it soccer over here, but it hasn't hurt the progress of the game in the States and Australia. It doesn't have to be a universal thing. Just a nickname.