Now, having compared the two videos myself and not found anything like this, obviously I had a look at it - and worked out the trick almost immediately. The comparison had the overlay ahead of the original by the same number of frames the whole way through from frame 1, but it was so faint that during normal viewing the difference was only visible in fast-moving parts, creating the illusion it leapt ahead in those parts. Easiest trick imaginable, could probably have been done trivially with film a century ago, and fooled someone who'd built a career and reputation around debunking faked videos along with many others.
(As for the White House video, that's a long story but the short version is that it seemed to be pretty much exactly what it purported to be, and the only actual "doctoring" was probably the obvious, intentional stuff like repeating parts of the video zoomed in.)
For the world you're describing to make sense people would actually have to demand video evidence to believe something.