John...
Why should a person comply with an illegal order from the police? If I am in my yard, and am not in the way of the arrest or any officers, I can legally set up 6 70mm IMAX cameras as well as a full array of lights and sound equipment as long as I don't shine the lights in my neighbor's windows at 10PM. I can then use the gear to record any police activity which happens on the public street in front of my house.
Quote: "If a law is unjust, a man is not only right to disobey it, he is obligated to do so!" - Thomas Jefferson
In this case it wasn't even a real law that she was disobeying but an ignorant police officer's assertion of a non-existent law/crime... The police do this all the time and largely get away with it because many people assume the police know more about the laws than they do... This is often far from the truth.
The woman who was arrested may well be anti-police, but I suspect she is more "anti abuse of police power". Most law-abiding people are very pro-police, but rightly fear the occasional officer who steps outside of the law, whether from ignorance of that law or from outright malice. It is in society's best interest that our police enforce the law... but it is not in our interest for them to make up laws they think should exist. Videotaping or photography police activity is one of the few means the public at large has to protect themselves because, lacking visual or audio evidence, the courts almost always believe the charging officer rather than the defendant.
Frankly, an officer who is acting within the law and who is following proper procedures should not fear the public's recording devices. Indeed they constantly say that we should not fear their recording devices if we are not doing something illegal... Whats sauce for the goose should be sauce for the gander...
Mike