C. australiensis is only remotely related to C. alboaggregatus which is a Phlegmacium in the Arguti group, species in that group have morphological similarities to the South American stirps Xiphidipus and sections Arguti and Claricolores.
Many southern Cortinarii don’t fit well into any of the northern groups and are usually only referred to as similar, much more study needs to be done, a good example would be the NZ species that would initially be considered to fit into the northern subg. Telamonia, most if not all have some deviating characteristics and it’s doubtful whether Telamonia in the strict sense occurs in the South Pacific.
Ref-Soop K., 2012: Cortinarioid Fungi of New Zealand.