The press coverage has mostly focused on the pointless show of physical force, the shackles and the prison-like detention. That should be criticized, but it sometimes feels like a tacit acknowledgement that all the workers were unlawfully present, or at least in some kind of "grey zone" (and thus did need to leave, just more humanely).

I'm not sure that's true. The B-1 forbids most work, including "construction", but there's a special set of rules for installing equipment sold by your foreign employer:

https://travel.state.gov/content/dam/visas/BusinessVisa%20Pu...

Many of those detained were employees of Hyundai's equipment vendors. A lawyer for some of those employees is alleging they were in fact compliant for that reason:

https://www.reuters.com/business/retail-consumer/lawyer-says...

If the DHS has evidence to the contrary, then it's had a week to disclose that and save some face. That they haven't may imply a significant fraction of those detained in these harsh conditions were in fact lawfully present.