Police have a lot of nasty tricks they can use to get people to talk, including the ability to lie about nearly anything. They can claim things are 'off the record' when they're not, lie about evidence or witness testimony, claim you being silent will result in them e.g. arresting your family members, and all other sorts of insane stuff. All completely legal.

It's easy to say don't talk, it's another altogether when you're surrounded by people whose entire profession includes getting people who don't want to talk, to talk.