Youtube allow you to embed their videos in your site, as they get a link out of it, and stay at the top of the rankings. Just stealing the .flv by hotlinking *might* piss them off, particularly if you are making money off the back of it. I know you said you don't charge your users, but do you have a totally free, without advertising website? If not, you are classed as commercial. The download from youtube admin function allows you to get the video you want anyway, as I said, you just need to host it. You said that your bandwidth charges would kill your project if you have to host this amount of data? With respect, if you have to hotlink, your project might need a rethink. Youtube will be able to pull the plug on you at any time, and could of course drag you into court.
If you really can't afford to host the vids, stick with the embed function, but if you are creating a site using 5000+ vids of theirs, I would expect to get noticed.
Just IMHO