My old highschool history teacher said that a reason for our close ties to America came about due to the fact that the USA was the only nation willing to send troops to our aid during the war (also we have ports which was important). How true is this statement?
The British released three divisions of volunteer Australians from the Western Desert to go back to Australia in the spring of 1942. These troops, the 6th, 7th and 9th infantry divisions played a key role in driving the Japanese army out of Papua New Guinea in 1942 and early 1943. They contained by passed Japanese garrisons in New Britain and the northern Solomon islands in 1943 and 1944 and played a role in liberating some of the islands in Indonesia in 1945, However, these were Australian troops. No British troops were sent to Australia, The United States sent their 32nd and 41st Infantry divisions to Australia in early 1942.
The Royal Navy did sent the County class heavy cruiser Shropshire to the Royal Australian Navy, to replace their heavy cruiser Canberra, that was sunk during the battle of Savo Island on August 10th 1942. The Brits also sent some Spitfire fighters and Beaufighter and Beaufort attack planes to Australia. However, some of the Beauforts were built in Australia and the United states sent more than twice as many warplanes to equip the Royal Australian Air Force than the British did. So, the British did send a limited amount of assistance to the Australians, but the Americans sent much more.
Sources: "World War II Airplanes: Vol. 2" by Enzo Angelucci and Paolo Matricardi pages 255-263
"Victory at Sea: World War II in the Pacific" by James Dunnigan and Albert Nofi