It was a glib answer. It's not wrong, though. Read Almeida-Sanchez v. US.
Reminder, though: we're talking about two different things: warrantless searches and documentation checks. It is, unfortunately, lawful for the police to demand your identification in a wide variety of circumstances, post Hiibel. (You still have the right to remain silent at those checkpoints, which is what the Youtube videos demonstrate).
Agreed on the 'search vs id check' distinction. The case law you mention involved someone taking it up all the way to the Supreme Court, a luxury not many have.
The reality is that these border patrol checks do happen, often well outside any reasonable range of an actual border and that they tend to be aggressive and searchy and done by people and to people who most likely did not take a close reading of Almeida-Sanchez v. US.
Reminder, though: we're talking about two different things: warrantless searches and documentation checks. It is, unfortunately, lawful for the police to demand your identification in a wide variety of circumstances, post Hiibel. (You still have the right to remain silent at those checkpoints, which is what the Youtube videos demonstrate).