How do I convince anybody to do stuff for me?
The answer is always the same... they do it because there is something in it for them! Family and friends do things because of the relationship. Businesses do things because they see the benefits to themselves.
I'd suggest you find a way of explaining how giving you access to the video will result in <insert what you will do for them here> and thus it would be a great value to them. Never lead with what they are doing for you, why would they care. Once they see the value in what you are bringing, they will be happy to give you what you need.