The reality is that while personality flaws and broken power dynamics may (but almost certainly won't) cause border police to charge you with some crime if you misstate "business or pleasure", absent any demonstrable intent of comitting a crime, you're unlikely to see the inside of a courtroom on such a charge, let alone be convicted. For instance, in the original post: saying you were in Antwerp for pleasure isn't going to get you a "Bureau of Prisons Number" without the satchel of smuggled diamonds.
I don't want to be misconstrued here; I'm glad we have crazy douchebags like this guy to stand up for our rights to refuse to answer questions, especially dragnet-style questions explicitly intended to trip criminals (and whatever collateral innocents come with them) up at the border.
But having said that, there's an element of the social contract at play here. The exact same logic this guy is using suggests that he also shouldn't answer the questions of police investigating crimes in his neighborhood. "Have you seen this man? We think he just shot up your neighbor's car."
Our society doesn't work if the police get absolute authority over us, and our protections against authoritarianism will degrade if people like this guy don't occasionally stand up for them. But society also won't work if everyone routinely refuses to cooperate with the police, who are dependent on our support to get the important stuff in their charter done.
I highly recommend "Cop in the Hood", a sociologist's writeup of a year spent as a Baltimore East Side patrol cop, for insight into all the crazy dynamics at play here.