This is very good advice. Name, rank, serial# sort of info and that's it. I like the police. But in this situation, you've got to keep your mouth shut. They've got their job. They're going to follow orders. And you've got to keep your mouth shut. As politely and respectfully as possible!
I know someone who the police picked up and questioned. When they asked the gal to take a lie detector test, she said she had to talk to her parents first.
Parents sent her to a lawyer—note if the parents had gone with her the attorney client privelege can be breached—must be private communication.
Lawyer told her to refuse any further discussion, and if arrested, to contact the lawyer. He said if they arrest you, they were going to anyway, but they could question you for hrs. before doing it.
He also advised her to tell her friends the same-no talking without a lawyer.