It looks like it depends on which visa you are applying for ;
The most popular is the Electronic Travel Authorization (ETA), which is an online visa that allows U.S. citizens to stay in Australia for up to 90 days Per Entry, for tourism or business purposes. It is a quick and easy visa option that we can help you get from the comfort of your own home!
The Visitor Visa, also known as an Australian Tourist Visa, allows U.S. citizens to stay in Australia for up to 12 months for tourism or to visit family and friends. It’s a multiple-entry visa.
If you are applying for the "visitor visa" you may be required to get the medical exam. For most of us we will just be getting the ETA for a 90 day stay and won't need the exam.