Australia signed up to the ANZUS treaty long before Keating was in power.
'The Australia, New Zealand, United States Security Treaty (ANZUS or ANZUS Treaty) is a 1951 collective security agreement initially formed as a trilateral agreement between Australia, New Zealand, and the United States;and from 1986 an agreement between New Zealand and Australia, and separately, Australia and the United States, to co-operate on military matters in the Pacific Ocean region, although today the treaty is taken to relate to conflicts worldwide. It provides that an armed attack on any of the three parties would be dangerous to the others, and that each should act to meet the common threat. '
Australia hasn't had full independence on military matters for a long time, having US troops/bases/subs in Australia makes little difference.
