What the actual tire pressure is after being lowered for offroading depends on the tire, its size, the wheel width, and the type of terrain being wheeled on. You're not even aired down until you get below 15 psi and most commonly 11-12 psi is pretty standard for most wheeling needs. I typically take my 35's down to 8 psi for the rocky trails my TJ is mostly on.
Yes, I agree. Just looked like in the video the tires were not flexing much. I think I know it depends on the tire rating C; E; D and how stiff the sidewalls are. Does Air pressure make you hop like that ?