Earlier quoted context omitted.
While it is true that you are physically at their mercy, provided you survive your encounter with the police (not by any means a guarantee in this country), you CANNOT be incriminated in a court of law for invoking your right to remain silent. You CAN be incriminated in a court of law for literally anything else you say. The winning move is clearly not to give them any more ammunition than they already have.
I think we all understand that part. It's the part where they can say anything happened and it's suddenly your word against theirs. So, irritating them can have consequences. The tactic feels fine for an interrogation room, where's everything is on camera. In the outside world, it's trickier.
A lot of people seem to think that not answering questions is going to aggravate the officer, and that’s not generally true in my experience. Assuming you’re asserting your rights calmly and not being belligerent, it’s well within the normal scope of behavior that they expert to encounter.