Obama could have issued an Executive Directive ordering the Park Service to "Stand Down" He has that power.
Presidential Directives and Memorandums Same as Executive Orders
Occasionally, presidents issue orders to executive branch agencies through "presidential directives" or "presidential memorandums," instead of executive orders. In January 2009, the U.S. Department of Justice issued a statement declaring presidential directives (memorandums) to have exactly the same effect as executive orders.
"A presidential directive has the same substantive legal effect as an executive order. It is the substance of the presidential action that is determinative, not the form of the document conveying that action," wrote acting U.S. Assistant Attorney General Randolph D. Moss. "Both an executive order and a presidential directive remain effective upon a change in administration, unless otherwise specified in the document, and both continue to be effective until subsequent presidential action is taken."