It came time to download some videos off YouTube to migrate them from one account to another... Dont' ask me why, that doesn't really matter. So, be that as it may - it is not as easy as it may seem. The FlashPlayer used to save them in your /tmp directory on Linux - but no more. The directory recommened at the link:
does not seem to contain anything resembling the video files one would expect either. However, then I followed a link specified at the above to get DamnVid and this seems to be working. The video ends up right under your ~/Videos directory hierarchy.