This is modeling based and although it does aim to factor in population aging effects, it does not account for the rapidly improving quality and accessibility of diagnostics.
Non-invasive diagnostic technologies are being developed ridiculously fast. Many are getting really cheap as well. Although I agree with the article that diagnostics should be made more accessible throughout the world, it is simultaneously important to realise that we do seem to be making that attainable.
Finally, there is also the problem of over-diagnosis. At a false positive rate of 0.0001, one in ten thousand people may incorrectly be diagnosed. On a population scale, that becomes problematic. So the problem might very well change from 'we are failing to diagnose 1/3 people with cancer' to 'we are telling one in 10000 people without cancer that they have cancer'. At this point it is very hard to tell which it is going to be.