Are you saying that dying of heart disease and cancer are over-diagnosed? Why does that matter in the context of this analysis? It's a comparison between CDC data and news coverage -- any "over-diagnosis" (or under-diagnosis) should be reflected in all datasets equally, so it doesn't really effect the overall review.
https://www.cdc.gov/injury/wisqars/pdf/leading_causes_of_dea...
EDIT: Take the data from the above table multiply the deaths by the number of "years of life lost" (65 minus the mid-range age for each column) and ignoring the 65 and older age group and I think you might see a better correlation with news coverage.
And to go along with that, I believe it is trying to ask the question "is it not just as important to follow the trends in so-called 'death by natural causes' as it is to follow trends for 'unnatural causes', at least as far as public awareness/good is concerned?"
Although the study is trying to do a larger scale comparison between the perceived and actul leading causes of deaths, it would serve it much better if it were to segment the results by age group.
A reasonable expectation for news coverage would be that coverage is proportional to deaths weighted by years of HealthSpan lost.
That cannot be exactly right. But coverage of loss of GrimSpan is a separate issue. If hip replacements and cataract operations are reducing the GrimSpan by increasing the HealthSpan that is a happier story than better infection control at Alzheimer's units increasing the GrimSpan. It is hard to state an expectation about news coverage of loss of GrimSpan