I think the answer to this question is situational at best. The configuration settings play a part in this as to whether or not it is set to have users upload videos. If they do i would assume it is the same as creating a document, in which you can share with specific people.
As for whether it is admins or all users, admins would have that ability within spaces and their own private profiles, and normal users, who do not have admin access to your spaces/places/sites/whatever the term is, would only be able to upload videos from their profiles, in which would fall under moderation (if you have that set up)
Hope this helps,
What Raul said. As long as you enable video upload for end-users they are good to go. Even if you don't enable video upload for end-users they should still be able to share the videos to which they have access.