2019 Update: These tools typically disappear, probably due to copywrite and other issues. So I have removed my suggestions below. Hopefully you can get the original video! It would be nice if YouTube/Google would allow for transfer of videos to different accounts, but until then... good luck finding the footage! That's why it's good to put video up on your OWN site, just so you have it down the road.
Sometimes I have clients like restaurants come to me and they have videos that have been posted on YouTube by their staff or customers, but they don't have a YouTube account for themselves. So I will setup a business YouTube Channel for their restaurant or business, and then we can upload videos to their channel for public viewing and also share the videos on their websites that I design. However, you can't "add" existing YouTube videos to a channel, so, since they have permission to use the videos, they can use this handy tool to download the videos so they can upload to their account: