They changed the scene to where he writes the order to kill Bin Laden down on a piece of paper ... and then shoves it down his pants.
That's believable.
Actually, Bill Clinton scribbles "do you think we should ever kill Bin Laden, or just send him to a tropical island.... mmmm, this hot babe here has a mouth like a vaccuum......" on a draft report but his handwriting is nearly illegible because he is busy being serviced by Monica..... Sandy Burglar stuffs the document down his pants but years later realizes he did not manage to destroy all the incriminating evidence of Clinton's, er, distraction, so the Burglar heads into the National Archives to cleanse the files.