I've had this random graphics stutter that would never ever show up in any benchmark at all, but weirder than anything else was that it also wouldn't show up in recordings made on that machine.

To save you the story of weeks-long debugging efforts - the problem turned out to the monitor. It was a Dell Ultrasharp 25", and (as I now know) they all had an issue where the monitor would freeze roughly every 20 seconds for a frame, because the monitor was advertising the refresh rate to windows as 59.95Hz but it was actually refreshing at 60Hz internally - the timing would get out of sync pretty much exactly every 20 seconds, causing the monitor to "pause" and freeze - which looked like stutter when playing games. The solution was using some kind of program(forgot the name now) which basically overrode the refresh information being sent from the monitor and forced windows to refresh at exactly 60Hz and no less - then it worked fine. But of course if you used it with a PS4 then you didn't have any way to do that and just had to suffer this stutter every 20 seconds.