Source control would certainly help establish a history of incrementally performing school work by someone when viewed by a highly technical examiner and when periodically stored someplace where a trusted 3rd party can confirm it wasn't all generated the night after a supposed false positive.
However, hundreds of hours of video is compelling to non-technical audiences and even more importantly is a preponderance of evidence that's going to be particularly damning if played in front of a PTA meeting.
With a git history it's going to come down to who can spin the better story. The video is the story and everyone recognizes it, so I expect fewer people would bother even challenging its authenticity.
It's only taking away their privacy if they're falsely accused.
And properly used you might not even have to relinquish privacy if falsely accused. A quick montage video demo and a promise to show the full hundreds of hours of video of "irrefutable" proof to embarrass the school district at the next PTA meeting might be sufficient to get the appropriate response.