I hope that the paper was published just for fun, not for serious discussion of the science.
Nothing is wrong about the statistical calculation. The p-value for correlation coefficient is indeed statistically significant. However, this superficial correlation ignores many confounding factors behind this correlation. I guess that it will be embarrassing to find out that even though there is a correlation between the chocolate consumption on national level and the number of Nobel Laureates, the Novel Laureates are those who consumed little or no chocolate.
In my first college lesson about the correlation, the teacher told me that before calculating the correlation coefficient, make sure that we were comparing two things that are related. If we try to claim there is a correlation between the growth of a tree and a growth of a baby, we will certainly be able to establish the correlation, but so what?
An excerpt from J. A. Paulos,Beyond Numeracy gives some examples that the wrong correlations are assumed.
“Children with bigger feet spell better. In areas of the South those counties with higher divorce rates generally have lower death rates. Nations that add fluoride to their water have a higher cancer rate than those that don't. Should we be stretching our children's feet? Are more hedonist articles in Penthouse and Cosmopolitan on the way? Is fluoridation a plot?
The odd results above are easily explained in this way. Children with bigger feet spell better because they're older, their greater age bringing about bigger feet and, not quite so certainly, better spelling. Age is a factor in the next example as well since those couples who are older are less likely to divorce and more likely to die than are those from counties with younger demographic profiles. And those nations that add fluoride to their water are generally wealthier and more health-conscious, and thus a greater percentage of their citizens live long enough to develop cancer, which is, to a large extent, a disease of old age.”
Unfortunately, nowadays, many articles in medical journals consciously or unconsciously presents the correlations between two things without further considering the confounding factors or the basis for the correlations. This is why we often see that a conclusion from one study is later totally reversed by the results from the another study.