This is becoming like the TSA domestic ID checks. TSA: You must have ID to fly domestically. If you don't, we cannot stop you, but we'll make it difficult for you, even if we have no authority to do so.
Border Police: You must answer my question on citizenship. You don't actually have to answer, but we'll try like hell to make you think you do.
The real issue for me, is that I would have no problem answering a question, in theory, even if I were not required to do it. The problem is that doing so gives the government tacit cooperation to encroach more and more. If all it really were, "Are you a US Citizen?" then, so be it; I'm very proud to tell it to anyone who will listen.
We all know, however, that this is not really it. The question is just a way for the police to gain access for a fishing expedition, which I would be fine with if they always caught criminals, and never inconvenienced innocents. Since this doesn't happen, if we must let criminals by, once in a while, to protect the rights of the innocent. I'm okay with that. The contrapositive is a much, much, worse outcome.