Amateurish digital optical fiddling would also explain the peculiarly washed out lights in the background, because every time you composite a new layer the overall brightness, gamma etc need to be re-adjusted and cumulative errors can arise. The same applies to the peculiar highlight on the fore-edge of the polished wood desk.
The overhead lights give each person a sharp-edged look; but if you enlarge the photo, you can see individual hairs out of place on Hillary's head against the dark suit of the guy standing to her right, and to a lesser extent, the guy with the short white hair-- only a few strands out of place. The guy almost out of the picture in the lower left is a mess of uncombed brown hair against the pixilated gray of the screen saver on the leftmost laptop.
One of the main reasons this photo is jarring is not so much the lighting, but the fact that Obama's body language does not at all convey that he is the top-ranked person in the photo. He is literally sitting in the corner in a smaller chair than the two men to his left, hunched over, and sportily dressed, while most others have either full uniform or some aspect of business wear. Obama is not in the least displaying any sort of leadership, even in his facial expression.