I don't know what you think a "large fraction of the population" equates to, but in this theoretical, 33% of the population being guaranteed to die isn't exactly ideal.
This is attributed to two factors: much more testing/screening than in most countries, which detects cancer at earlier and more treatable stages (though at high cost), and most new cancer-related treatments are developed and available in the US first so any resulting reductions in mortality show up in that population first.
As an example, my "anecdote" was cured of terminal cancer by an experimental drug therapy in late trials. Several years later it is FDA approved and becoming available in the rest of the world but at the time the only people receiving that treatment were in the US and it was correlated with a material increase in survival rates for that kind of cancer.
I don't know why you're quoting "anecdote," you gave a textbook example of anecdotal evidence, which is not data. My uncle Bob survived testicular torsion, therefore all uncle Bobs will survive testicular torsion. How many people in the U.S. with that exact same cancer did not receive that particular experimental drug therapy? Did that one person, or even all the people included in the trial, change the survival rates in America during that time period?
The overall cancer survival rate in the US for males is around 67%, which is extremely high even by developed world standards. It wouldn't be possible to have a survival rate that high if a large fraction of the population was excluded from treatment.