The photo didn't need to be shared in the first place. No one knew it had been taken outside of a small group of White House insiders...
Here's how easy it would have been to do an honest photo: a picture is taken with Obama in the room (later) - with a cut line about how they're 'watching the tape - and several replays' of what happened... could have been one minute later, one hour, or 12 hours later. It's the official picture from that day - and it's the truth. The suck up liberal press wouldn't push the issue. Obama IS a democrat after all. The answer, 'that day ' would be accepted.
The picture would stand - and it would be historically accurate.
The act of faking a photo - with that many high level people involved in the fake, is a form of control... it's psychologically powerful if the goal is to compromise people who are usually ethical. People who went along with the fake have two choices - two things they can tell themselves... - either they're not as ethical as they think ( a choice they won't make) OR the public can be lied to... this time - AND in the future.
The first time a man kisses a woman other than is wife there's a great internal moral debate going on within him. It's a greater debates than he'll the next 10 times he's unfaithful. People justify cheating - and once compromised, the ethical debate starts looking silly - - the consequence of being compromised.