Just got this from an F-16 pilot I know..
“I’m assuming they used 2-seat F-16’s and put a photographer in the back seat. We used to do that all the time at Edwards to take both still shots and videos of some of the flight tests we did. We even had a career field for professional airborne photographers.”
So it appears that they could have used Hand Held cameras from the F-16, but they would have to be 2 seater versions, something that should be verifiable from the videos that were shot.
The other point is that the military does a LOT of airborne photography, missile tests, flight tests, etc. So they would be more than likely to keep the job “in house” since they have professional aviation photographers.
My common sense has stood me well in making accurate appraisals. For example, it told me in the early days of the primaries, when most here were certain that Hillary would be the nominee, that indeed Hillary was far from guaranteed. I warned folks not to fall for the "Hillary" bogeyman, and I was proven right. My common sense told me in the early breaking hours of the Cptn. Phillips rescue, when FReepers totally bought news reports that he'd jumped a second time and thereby initiated the rescue, was bogus -- and I was right.
My common sense tells me now that the "photo op" angle is a ruse, and I bet I'm right about that, too, though it may be a long time or maybe never that we find out the truth. But common sense says this is bogus: why prohibit it from being announced in advance, when people would have welcomed the sight? The pres wasn't on board and therefore it was no threat to national security to announce it. Why the close flybys as seen in bystander videos? Why the timing on a workday Monday morning? Why only fighter escorts, and no reassuring photog planes? Why do it when the skies are hazy?
As I've said, I don't have any ideas as to what it WAS, only what it wasn't. However, two things come to mind. 1: It couldn't be announced in advance because it entailed something secret, or 2. It couldn't be announced in advance because no one knew it was going to happen -- that something really screwy and scary happened and there was a royal hustle to cover ass entailing a lame "photo op" scenario.