Instead, it's better to just come out and say it: while watching the swimming event and cut-down highlights of the opening ceremony, there were moments when we could almost have believed we were looking not at a projected image, but rather through a window direct onto the Olympic Stadium or Aquatics Center itself.
Mr Obama, who was senator for Illinois and lived in Chicago before his election to the White House, will be the first sitting US president to take on such a direct role in an Olympic bid.