Indonesia claims that once asylum seekers leave its territorial waters they become the business of other governments so that attempts to turn them back are inappropriate. This seems to be an attempt to thwart, or manipulate, attempts to resolve the asylum seeker/economic refugee/queue jumper problem. These illegal immigrants do not seek to reside in Indonesia but want to live in Australia. If they are prevented from making the last leg of their journey they will not attempt the earlier stages of their journey and neither Indonesia or Australia will face a problem.
If Indonesia wants continued economic aid from Australia and good relations with Australia then it needs to cooperate to end what is for Australia a significant problem. It is not a matter of Australia having to agree with every counterproductive Indonesian view. Generally the cringe in Australia towards Asian countries is foolish from the viewpoint of our national self-interest.
Nor should Australia feel it is on the back foot because it has intervened in the past to stop Indonesian terrorism in situations such as East Timor. Indonesia needs to look at itself (and its current behaviour in areas such as West Papua) rather than suspiciously casting its eyes on neighbours who are in fact reasonably good friends. Being prickly about issues which do require international cooperation is unhelpful.