She was actually picked up by the French, although Australia was heavily involved in the rescue effort (the girl got herself in trouble on the border of Australian and French maritime rescue zones - Australia had better aerial resources to precisely locate her, but a French vessel was close enough to pick her up. But the situation is different.
Her life was in danger, making her a 'distressed mariner' and therefore the response to rescue her fell under the general 'law of the sea' - that mariners and maritime nations respond to rescue each other because you'd expect the others to do it for you.
In the case of the MV Akademik Shokalskiy, they weren't actually in any real immediate danger. They could have stayed icebound for quite a while quite safely, waiting for the opportunity to leave. That changes things - there's a difference between mobilising resources to save people who are in actual danger, and doing it simply because they are in an uncomfortable situation.
Thanks for the info.