Except (as I hear it) that's not even true in the US. Apparently, it's not enough to stay silent - you actually have to say that you are exercising the right to be silent, otherwise they are allowed to infer guilt from silence.

In a very similar way, if I were ever detained in this manner in the UK, I'd be very likely to say "I am not refusing right now to answer your questions. However, since I cannot trust you to tell me the truth about my rights and responsibilities, and because of the power imbalance, I will wait until I have independent legal advice before participating any further in this interview".