That is not to diminish the problem. Over-reliance in purely statistical methods has gotten us in trouble -- in some fields more than others. Probably the main issue is that the fields affected are ones that happen to the biggest right now, with potential impact on quality of life and public policy.
Fields that are doing a better job of weathering the storm, such as physics, have tended to have a larger tool belt, and the use of statistics is kept in check by other methods such as the development of theory, and the ability to study problems from multiple vantage points. Also, physicists can choose our battles, and only look at problems where more robust statistics can be used.