The headline is shocking when one consider the steep rise of cancer since 1945. If it was luck, then how it could change over time?
we need to be careful that we are comparing apples with apples when comparing cancer rates between different countries or time periods. We have higher rates of people reaching their 70s and 80s now. And in addition to increased longevity, we also (in developed countries at least) have a higher proportion of our populations being older.
This is why we use an "age standardised cancer incidence" rate, to account for differences in the population makeup.
I'm not sure if the age-adjusted rate is much difference between now and the 40s, but if it is then I would expect it to be largely based on the dramatic rates of tobacco use in the couple of decades after WW2.