They can say anything they want and it's up to the FAA to stop them from enforcing it. So far the FAA has said nothing significant about it (except on paper) and the FAA is sending the message to local agencies and communities to carry on, we'll let you know if we have a problem.
The way most laws work in America if you don't defend them vigorously, they soon lose their power and become unenforceable. If you have a couple of legal cases where the FAA has put down any local government that has proclaimed "NO DRONES" I would love to see it. Honestly, I think many governments know they don't have that power and have been told they don't have that power by their own legal teams but have chosen to do it anyway based on the thinking they have "states rights", the law is not settled, and FAA is absent. Just like there are many jurisdictions all over America that ban curse words in public and arrest people for it. If I knew I could go to that park and fly a drone against their will and get fined/arrested and could challenge it in court with a competent legal team to create a meaningful legal precedent, I would do it. But unfortunately it's not that easy, there are tricks and loopholes abound working against us. My case would be dropped, the fines rescinded, I would be given a trespass notice, and they'll just pop the next guy.