We had some coaches that had the same issue, but fortunately many of them didn't. As a state, we get just over half of the games on video. It often requires follow-up by the crew to request the video, but they do it.
I would suggest communicating as much as possible to your crews to not share any video outside of their crew. If they want to share individual plays with others in the association that should be fine. Make sure this is a clearly communicated policy and share it with the coaches. If they have an association definitely work with their leadership. The key once they start providing video is to back up what you said you would do to control the distribution.