 PLOT: SPOILER: Either Lawrence is a poor doctor (which considering  where he places the tourniquet might well be the case) or Jigsaw  ingested some chemical to make him seem dead (which would still be a  plot hole because its never mentioned if he did), but dead bodies  do not, under any circumstances, look like live bodies. Simply by  breathing Jigsaw would have given himself away, not necessarily as  the killer but certainly as someone who isnt dead. And their  circumstances cant factor into it (i.e. they are too frightened to  notice), because they spend time in the film contemplating the body.  (This is in fact tied up and clarified in _Saw III (2006)_ (qv)).