It's truly sad when something like that happens...people need to learn cemeteries are something to respect! It always makes me want to cry when I find a cemetery either vandalized or badly in need of repair. I don't think there's anything wrong with offering to help...try to offer your help directly to the cemetery association. Usually the local library or historical society will have records of who is in charge of the cemetery. If they don't, city hall will.
As far as the talk of the police closing it to the public, I don't think they legally can. If it's a public cemetery, they can't suddenly keep people from going to it. They COULD put up a gate, which they could lock at night...if they really want to...but most cities find that starts to become a pain.