It is a ship owned by a Danish company, Maersk. Its officers are Europeans and its crewed is Asians. It is registered in the Republic of the Marshall Islands, an independent country. It is not a U.S. ship, either de facto or de jure.
http://www.freerepublic.com/focus/f-news/3284923/posts
US Navy to accompany US-flagged ships in Persian Gulf after Iran seizes vessel
foxnews.com ^ | 4/30/15 | foxnews
Posted on 4/30/2015, 12:21:26 PM by ColdOne
U.S. Navy ships will begin to accompany U.S. flagged commercial ships as they travel the Strait of Hormuz, a defense official confirmed to Fox News, on the heels of Iran seizing a cargo ship.