VLC???
Okay, some findings: I took the suspect MP4s back to the BI machine and they don't pulse and jerk, so yes, this symptom is machine-dependent, and yes, my regular "work" desktop which I've been bringing the clips to for editing is kind of wuss, it's a quite-new i3 with 8 gigs of RAM, but that should do fine, shouldn't it?
And this: on this wuss machine, if I set the video player to "repeat" and loop the videos, the jerkiness does not occur, only on the initial start-up. Could it just be that this machine has trouble "spooling up" these short clips, and then once it gets going, it's fluid?