Ahem....your thinking is good, but the problem is you might get to spend a night or weekend in jail if you overly "invoke your rights", while things get sorted out.....the police DO have the right to question you.
I’ll take a weekend in the city or county as opposed to years in the state penn. And no, if you watch that you will see why you shouldn’t talk. Watch it and come back. They DON’T have the “RIGHT” to question you.