Australian National Airline College is approved by the Civil Aviation Safety Authority (CASA) to train pilots.
So in practice, ANAC conducts the training according to the CASA syllabus but CASA conducts the theory exams and flight tests and it is CASA that issues you a licence.
ANAC has its own Approved Testing Officer i.e CASA allows this person to conduct flight tests on its behalf.
ANAC is a Registered Training Organisation (RTO) approved by the Australian Federal Government to train overseas students:
Specifically by Australian Skills Quality Authority (ASQA)
Information about the Australian National Airline College can be found at the Commonwealth Register of Institutions and Courses for Overseas Students (CRICOS). The CRICOS code for the ANAC is 02530B