Of course they do. It’s mind-boggling stupidity. You’re more likely to die in a car accident on your way to the airport than to have a run in with any of our wildlife. Between them my four grandparents lived in this country in excess of 300 years without dying of vicious fauna; I’m certain you’ll survive a weeks-long vacation.
According to this report, 1,735 people were killed by animal attacks in the U.S. (excluding dogs, which are not wild) between 1991 and 2001, for an average of 157.7 deaths per year. Given the stats in this previous post) and the 6 ant fatalities in 20 years here, there are just 3.8 deaths per year in Australia; adjusting for population (311.6 / 22.33) brings that up to 53 deaths per year - which means that, per unit population, three times as many people die in the U.S. every year from animal attacks.
Admittedly, Australian deaths are not from a very comprehensive source and the years covered are different (but lets assume a constant fatality rate), and the population figures are current (another assumption about similar population growth rates); but it doesn’t appear that Australia’s reputation for deadly animals is warranted (except for maybe snakes, many of which do top the list - but they also haven’t actually killed anybody, at least between 1980 and 1990).