Sure, America's healthcare system is deeply flawed, but it's important to attack it on fair grounds. We can't solve a systemic issue by raising claims and arguments that aren't supported by evidence.
EDIT: Furthermore, identifying early stage cancer is an extremely problematic and difficult field regardless of healthcare system and country. In America, we currently screen asymptomatic healthy adults for breast cancer and colon cancer. We screen people with a smoking history for lung cancer. However, the benefits to overall mortality of these cancer screening tests is controversial.
While in theory identifying stage I cancer should result in improved overall mortality, the data doesn't clearly show that. Take a look at length-time bias (https://en.wikipedia.org/wiki/Length_time_bias). It's possible that a substantial portion of the cancer screening that's done in America (and the stage I cancers found in Australia) selectively identify indolent cancers that are unlikely to be harmful to patients.