Honestly, I would believe it. I haven't watched the video and I can't account for it's authenticity, but I've heard the complaint before on the Smashboards. It wouldn't be the first time a game had this problem either. When Starcraft got a patch that allowed replays to be recorded, sometimes the replays came out innacurate. The reason:It doesn't record a video of the match, it records instructions for a computer to recreate the match. It's just 2 computers on the same stage putting in the same commands at the time specified to recreate what happened originally. Now this works most of the time, but on occasion the computer records a command wrong, or the timing of the command wrong, or just for some reason doesn't record any commands. This results in matches that come out weird, and buggy and will resemble your match only up until a certain time and then falls apart.
It's not unheard of, and I'm sure sometimes the computer gets it wrong for smash bros too. Not the end of the world.