Preserving Rural Resources Act of 2013 - Amends the Federal Water Pollution Control Act (commonly known as the Clean Water Act) to replace a requirement that a permit be obtained for any discharge of dredged or fill material into the navigable waters incidental to any activity having as its purpose bringing an area of such waters into a use to which it was not previously subject and where the flow or circulation of such waters may be impaired or the reach of such waters may be reduced with a requirement that a permit be obtained for any such discharge that is not currently exempted from permit requirements.