I've actually done that once, when I was an unaware college student/sheeple.

Close to the Canadian border, the Border Patrol pulled me over and I was going over 90 on the interstate. But they can't write speeding tickets so that wasn't it. They claimed I had crossed the border illegally and suspected me of smuggling drugs/people across. I did not have my passport on me, and apparently they could not look up my citizenship info from everything I'd given them (DL, SSN, student ID). In retrospect, I suspect this was BS and wasn't their main concern.

They asked me to drive with them to their station and continue the questioning there, and I did. I had done nothing wrong, but I wasn't sure what would have happened if I had refused (probably arrested).

They were really fixated on my being a smuggler and their questioning was, as you described, crafty. Thankfully, I did not trip up too badly and my parents were eventually able to fax over citizenship docs. But what really cleared it was allowing them to search my car. I did not think anything of it at the time, but I would not allow that today.