I had a friend who recently got in trouble with the police. He literally didn't do anything wrong. He doesn't drink or do drugs, but he does seem naturally spaced out most of the time. What happened is he made his situation much worse by talking to the police. All they have to do is assert you are on something to arrest you. It doesn't have to be true and nothing you can say will help that.

Same thing goes with a false rape accusation. Everything you say can only be used against you. Nothing you say to the police can be used for your defense. An officer using your statements in your defense is considered hearsay and isn't admissible in court.

If you get into an interaction with the police, regardless of the reason, nothing you can say will ever help you. If you are going to be arrested, so be it, keep your mouth shut and deal with it. You can't talk your way out of being arrested. You only ever talk to your defense attorney. Doing anything else is just shooting yourself in the foot.

In the following video a law professor goes over the 5th amendment, why it is important, and examples of seemingly innocent statements were used to convict people. Watch it for your edumacation.

https://www.youtube.com/watch?v=ptqyKH6-whM

Dave Chappelle did a skit on this. It is humorous of course, and has limited educational value, but he was actually trying to build awareness about the 5th amendment so people would actually be aware of it before getting into bad situations.

https://www.youtube.com/watch?v=mdeo7Q2E5cE

EDIT: this is also relevant to domestic violence charges.