> "illegally crossed the U.S. border"

What, precisely, does this mean? I don't think it means "crossed from Mexico or arrived on a small boat". I think it might actually mean "at the border interview, they said the purpose of their visit to the facility was 'business meetings' rather than 'work'", and the legality hinges on the precise knife edge of the W word.

It would be really, really useful to clarify exactly what the rules are for someone entering the US under a visa waiver for business purposes are, because I don't want to see my co-workers thrown in a gulag.