Okay: This is much ado about nothing, but four points:Wow. Your points add up pretty well. If you ignore the smoke, it looks like the President is merely shouldering the weapon, and neither aiming it or firing...he is merely holding it up to his shoulder.
1. President Obama is depicted firing an over and under shotgun. Why is there a wisp of smoke about 8" back from the muzzle? There are no gas ports anywhere in that area on an over and under (or a side by side).
2. That appears to be a 12 gauge, presumably loaded with skeet rounds, which are low velocity. Still, the way that the Prez is holding the gun, wouldn't the recoil cause the but to rise up and over his shoulder, smacking him in the nose with the receiver? and, you want the butt snugged tightly into your shoulder, since you don't want any free travel after the shot: don't let the gun bounce" against your shoulder or you get bad bruises.
3. At least for me, I want my trigger hand above and around the receiver to keep this from happening. I think this is true for most shooters. Also, along the same lines, his posture is very vertical: when I, at least, shoot a 12 gauge, I lean into it to help control the recoil. I think must folks do also.
4. As you previously pointed out, the sight line is all wrong: his eye is below the rear sight and in order to see the front sight, he would have to dip the top of his head and look out under his brows. Which he is not doing, so he cannot see either sight. Even with the "point and shoot" technique, you have to see the front sight,so it is unlikely that he is aiming...he is simply holding the gun.
I think the President was photographed holding the gun "offhand", not tucked away, as if he didn't really want to get too close to the icky thing and then the smoke was photoshopped in afterwards.
But, as I say, much ado about nothing in the overall scheme of things.
The Czar did zoom in to see if his finger was even on the trigger; it is, although curiously there are few high resolution files of this picture on the web. The Czar agrees that one could take many photos of the Czar in an identical posturebringing up a weapon to the shoulder just to see what it looks like, but not actually aiming or firing it. Of course, our finger would never be on the trigger.
As you say, it would be easy to take such a photo and P-shop in the smoke and fix the trigger so that he was pulling it. There are plenty of folks who can analyze a photo and determine from the pixel whether it was digitally edited; let us wait to see what they say.
By the way, the shotgun appears to be a Browning Citori 725. But the important bit: the Browning does not have a vented port barrel; what is that smoke coming out of the top of the barrel? And why would anyone bother adding smoke in? If you want to see a few slo-mo clips proving the Citori does not vent gas out the top as shown, the Browning website has them. Incidentally, people are also asking why he was a choke in the upper barrel but not the lower. Good question.
Frankly, there may be too much smoke coming out of the shotgun anway, unless he is using some really badly made reloads.
Seems that even if that is the President firing a shotgun, the picture is still outlandish and exposes this as a pure stunt that, well, backfired.