A video won't show a fault (unless it's a shockingly obvious framerate dip) and judging by the OP, he didn't exactly come across as convinced there was any issue in the first place.
This is why it was crazy to scream fault, and suggesting throwing money at the thing to 'fix' it was beyond daft. It's nothing to do with the framerate and everything to do with perception. Sure, there's people in here that game at smooth framerates on pc and say GTA runs 'fine' for them... well perhaps that's because they understand from the start that GTA on PS3 is simply not going to run at the same kind of framerate as pc games do, hence the game is no more or less than they expected.
Again, it's all about perception, the same chocolate milkshake can to one person be perfect, and to another the most disgusting thing in the world. What changed? The milkshake? Nope, exactly the same in both situations, what changes is the perception. When you start going past 60 frames a second, then I can see the argument that people are being over sensitive or making an issue for no reason, but when a game runs below 30 almost always and also suffers noticeable drops, it can easily range anywhere from noticeable to extremely jarring, depending on the person.
Best bet here is if at all possible to see the game running on another console and tv, surely one of your mates must have the game as well?