I think allowing unrestricted taping of minors is a bad idea. How do you make sure it is the kid's parents? Is it the job of the other kid's parents to verify this? I don't think so. Is it the TD's responsibility to patrol this? What if one parent is biological but has a "boyfriend" who is doing the taping? And that guy is a creep whom she has known for a week?
The onus should be on those who want to shoot the video. They should present their credentials to the TD, the TD should ask the other kid's parents, and only then allow the request.
As a good example of what might happen, there is the recent case of the high school pole vault girl. Her pictures led to several obscene comments leading to huge distress to the parents.
Even journalists have limited First Amendment rights, and their own code of ethics. For example, they can film a general scene but cannot keep focusing on particular people. Has nobody noticed how faces are blurred in such situations? What makes anyone think that they can focus on a minor female kid for 2 hours and claim it is their "right" and then out it up on the Internet for anyone to mock and creeps to pursue? Totally irresponsible attitude of entitlement and a contempt for others' feelings.