https://www.youtube.com/watch?v=6wXkI4t7nuc
You're being recorded, both audio and video, from the moment you enter the building. Making a false statement, even accidentally, is a serious crime. They, of course, are allowed to lie as much as they wish with no repercussions. Ask any lawyer: making any voluntary statements to the police is a bad idea under any circumstances.
Furthermore, my travel within or without the United States is no business of the government's, as evidenced by the fact that there's no law requiring me to provide it to them. Every time this has happened, I have been allowed in to the US. Every time.
The troubling part is that this is really just a demonstration of what the police would do if Terry v. Ohio or the 5th Amendment weren't in place.
They see absolutely no irony in harassing an American, on American soil, under the banner of "protecting America".
Being late, I can cope with. The fact that large federal law enforcement organizations like CBP fundamentally don't get why we have basic rights is the truly scary part.