This was an interior immigration checkpoint, not a border/customs check. This area of the law is unclear. DHS statutes and regulations seem broader than the applicable constitutional law cases. The Supreme Court says you can be "briefly" detained to ask you about your immigration status. The DHS claim they can send you to "secondary" for more extensive interrogation seems to violate that case law unless they have an individualized reason to suspect you are not a legal US resident.
They cannot search a car without probable cause. They cannot take someone into custody without probable cause.
I did some googling and it seems there are people doing what this video shows and recording the incidents. In every one I found, DHS eventually gives up and waives them through.