I'm not a statistician, but I know and work with some real statisticians. They would cringe if they read that article.
The problem, they would probably say, is the ready availability of computer software that makes the statistical calculations easy for anyone to use even if they are ignorant about the proper methods of statistical analysis. Because a bunch of analysis methods are available that can produce different results, many invalid results have been published by people who used stat analysis software to "go fishing" for an analysis method that yielded the answer they were hoping to get. I know enough about statistics to recognize that I don't understand which ones may or may not be valid for a given case.
Another problem is the lax editorial standards of that journal Psychological Science. They probably don't check the statistical analysis submitted to them.
And finally, science can never prove anything. It can demonstrate (sometimes convincingly) and disprove, but can never establish genuine proof. I was trained to stay away from that word.
