A couple clarifications.

All major roads along the four states bordering Mexico have "Border Checkpoint stations" about fifty miles into the USA from the border.  These are what forces illegal Mexicans to go cross country instead of just using the roads.   These stations are in addition to the Border stations at the actual border.   All cars and trucks must stop at these stations, and it is not unusual to see very long lines and 30 minute wait times.

They have asked me the same routine questions.  "Are you a US citizen." "Pop the trunk."  Then you go on your way.

The way agencies know if someone is a citizen if they don't show papers is to get some data items, address, date of birth, so forth, then run that through their computer.  US citizens are not required to carry any papers or proof of citizenship.  The driver of the car should have a drivers license.

Not defending what these stations do, actually they are extremely annoying to people that live in the area who have to routinely deal with them.