It does not assess the distribution of presentations by stage, it notes a 14% gap of US population coverage (i.e. people entirely unaccounted for in the survival statistics), and if you refer to tables 6 & 7 it's clear that the US overall has slightly worse net 5-year survival rates than Australia for some cancers, and slightly better for some.
In practice, the standard of care available in both countries is very high. It merely remains to present for treatment in time, or whether the system sees you at all.
I must add that focusing on death promotes the repugnant idea that mortality is the only cancer outcome worth assessing. It is not. Taking a moment to considers humans as people, not a pile of potential corpses, will I hope trigger consideration of the quality-of-life consequences of late presentation: people suffering unnecessarily for considerable time, where the incentive for them to suffer instead of seeking treatment is socioeconomic.
Moreover, irrespective of eventual outcome, such cases are more time and resource-intensive, which (along with rent-seeking organisational cliques) is a contributory factor to the fiscal inefficiency of the US health system.