Of course they'll shoot it down. The police don't want anyone filming them murdering the protesters.[/sarcasm]
But in all seriousness, I agree with being upset and protesting as a way to show the magnitude of how pissed off people were ... but they need to be more worried about people trying to infiltrate the movement who want to cause violence than police officers. There are many anarchist groups that are frothing at the mouth for this kind of movement; get the police to act against you, trick the protesters into pushing back against the police and take advantage of the ensuing chaos to do whatever the fuck you want.
If I can figure out how to do it pretty easily ... then I'm sure there's others out there who'd want to take advantage of it, too. Nothing provides better cover than a large group of people.