Protecting States, Opening National Parks Act - Directs the Secretary of the Treasury to reimburse any state for state funds expended for an activity conducted in FY2014 during the federal government shutdown that was necessary to operate and open to the public a National Park located, in whole or in part, within the state. Requires any such activity to have been: (1) authorized under federal law, (2) conducted in a manner and at a level not substantially greater in scope or cost than how the activity would have been conducted by the federal government, and (3) not a settlement of or defense against a claim of liability on the part of the state.