Safe And Fair Environment on Highways Achieved through Underwriting Levels Act of 2013 or SAFE HAUL Act of 2013 - Revises certain minimum financial responsibility requirements to increase from $750,000 to $4.422 million the minimum level of financial responsibility sufficient to satisfy established liability coverage for motor carriers or motor private carriers providing property transportation. Requires the Secretary of Transportation (DOT) to adjust such amount annually for inflation relating to medical care.