Yet another variable that would need to be taken into account, thanks Tiki.
This is why it is wrong to present a conclusion from a study that is based on a very weak correlation. A study done on the rate of infant mortality and the ownership of brown dogs, could show a correlation, in countries where there is a high ownership of brown dogs, there is also a correlating increase in infant mortality, (although a weak one).
Is this weak correlation worth studying, probably not, could a conclusion be drawn from the weak correlation, no, unless you have a bias against brown dogs.
This is a deliberately ridiculous theory, but no more ridiculous than the study in the OP.