I think they should film it. The administrators just don't want to deal with the aftermath of a publicized video. It's easier for them to push things under the rug when there isn't video proof.
This is exactly what it is. They are scared of transparency and being held accountable for anything.
They cannot stop anyone from filming. Policy does not Trump law.
Even in Town Halls and such, when they have policies "no filming, no cell phones, etc" that policy if for THEM to follow, employees.
The public does not need to adhere to their policies. If a Town worker films you with their cell-phone (on the job), you can FOIA their phone and even get their personal pics off of it.
They do not like those who know their rights and push back, as it shows they basically have zero power over anyone. Cops as well.
They cannot tell you where to stand, etc... (Especially if they don't have crime-scene tape up). Call 'em a kvnt (freedom of speech) and just keep standing and filming them.