I know we just recently got into a bit of tussle elsewhere, but I think I mostly agree with you here.
The uh, the 'morph-cut', when his hands shift and kinda melt?
Look above his head when that happens.
The lighting and shadow on the trees in the background changes.
Its all one way before that happens, and its all another way after that happens.
... I think he literally stroked out, while they were filming this, thats why the morph cut is there, and if some body wanted to try to model the scene, the oval office, geopositioned right, with the sun, they could probably estimate how long it was between these two shots they merged together... or timeskipped between.
I don't think his face is completely fake, I think it may have some kind of... correction applied to it, to try to minimize the droopiness of ... what you can see in his face today, from the 9/11 memorial.
Sorta like how and instagram filter morphs your face... and a frame stabilization effect tries to keep objects centered and just boink the frame itself around...
Something like a face stabilization effect, if that makes any sense.