Even without a hard copy, how would you be able to view the video but not download it? YouTube, Vimeo, etc. are all downloadable with a variety of Firefox plugins & desktop applications.
Let's say that you can solve that problem, perhaps there's a solution out there that I'm not aware of. You still have the ability to record it at the same quality it plays using CamStudio or any other kind of screen recording software.
Ok, so let's pretend you've managed to block any kind of downloading, any kind of screen recording program and any kind of site vulnerability. If I were the kind of person who wanted to download photos to start a scandal, I'd just take a picture of the screen with a digital camera. Sure, the resolution might suffer slightly but with a tripod and a little trial and error I bet I could get them pretty nice.
I like the idea of being in control of when they're deleted from the server or having a time limit, I just don't think it's possible to control where the content ends up.