Per CurrituckChamber.com, no overnight camping is permitted on the beaches. So you know, even at official campsites up and down the Outer Banks (quite a few of which are in The Cape Hatteras National Seashore) do not permit camping on the beach. Tent camping is permitted in designated areas. This is for safety reasons (variance of tide lines, etc.) and for the safety of nesting animals like sea turtles and the like.
Hope this helps (although I know not the answer the boys were hoping for),