"Saying little" means providing only the absolutely necessary information. If you were in a self-defense situation and your attacker threw his weapon in a bush, you want the police to know that so that they can find it. If there were witnesses who can corraborate your story then you want the police to talk to them before they disappear forever. If you need medical help, you should ask for it.
I'm guessing, saying nothing infers guilt whereas saying 'I can't remember...' (or similar) leaves room for manoeuvre at a later date?