It is being called a 'secret' filming, not because they are being secretive about doing it, but because the actual film will be kept privately, and not released to the general public (which is odd because I've seen most of it in stills in the Daily Mail). Lawfully they can film his execution, and have done so, firstly to prove that he is dead, and secondly for 'historic' purposes (so your grandkids can watch it in school). And I doubt any Iraqui observers had video phones handy.