Respectfully disagree on your last point.
Obama claims and is portrayed as a huge Lincoln Afficionado. Should he have not known there were different versions? And possibly that the biggest difference between them is the presence of “under God”?
So either Obama isn’t as big of a Lincoln scholar as he claims to be (and got manipulated. By Ken Burns) or he knowingly agreed to read the Hay copy without “under God”.
Maybe Burns used this version because he knew there would be no objection from the spitehouse? First time he felt he could get away with it.