Dan/Ginger,
I would suggest Add a Resource -> File to upload the original video for students to download - this doesn't embed it to play on the site, but that's not what was asked for.
And then Add an Activity -> Assignment: Upload single File for the students to be able to repost it for the teacher to grade.
http://docs.moodle.org/en/Adding_resources_and_activities
Not an activity I've tried myself I have to say (Primary children don't tend to have much access to video editing, and when they do, the files are on the local network rather than adding them from Moodle :D) but this would seem to be the logical way to achieve what Ginger was asking about - I have used the same method with Word/Publisher/Graphics files with 8-9 year olds.
HTH Richard