Someone should also find out the names of any civilians aboard AF1.
It could have been with an automated or remote-operated camera. Or from a nearby helicopter which wouldn’t have attracted any attention.
If the photos were taken from an F-16, it was very likely a two seater, specially outfitted for air to air photos.
But, if I had to guess, I'd guess that there was another aircraft up there doing the photography.
The Air Force has done this sort of thing for a long time. One of the prototype B-70s was lost during a photo shoot highlighting aircraft with engines from General Electric. I've seen the surving B-70 at the Air Force Museum at Wright Patterson AFB, although it was still outside then, over 20 years ago.
I imagine they probably have a camera pod on a hardpoint.