Or you could say something useful to help OP.
Let me walk you through my thoughts, since you clearly have nothing better to do and have the time to read this:
Since OP did not specify whether or not the video was private, I have to assume the video is public. I would absolutely hate if someone was making a video about how bad my site was optimized. I would
especially hate if that video was free for anyone to search, to the point I'd demand the video be taken down regardless, and probably wouldn't hire whoever tried embarrassing me into improving my site.
That is one of my intentions actually, for the video to get under their skin to the point where they want to take action. Say for example you own a dinner and i go to your store and night with my camera and take pictures of the rodents having a party in the kitchen and post that on youtube, would i have to take that video down? Isn't that what the media does anyway???LOL, i guess i will just start a media company then 
Good points!
Stating the facts is polite smearing, and unless done privately, I would assume it's a hostile campaign. One should not have to be demanded to take down that kind of video if it was public; if it was private, then there is no issue and can be looked at later as a reference. With permission from the owner of the business the video is analyzing, it can even be used as part of a portfolio.
If public, the video should be taken down regardless of whether or not its demanded. That's business etiquette. Why place on the public domain a video showcasing: "here is my client's piece of shit site. gaze in wonder at their amateurism."
LOL, well if they are a client then i wouldn't do that. Here is something to think about, there are websites that display mug shots of people that went to jail, if you want to get the mug shot pic off their site, you gotta pay! Just a side thought.
DamageX, did you even understand what I was asking OP in my post? Are you cruel to your clients, or do you need to improve your reading comprehension?