Earlier quoted context omitted.
There is no exception in the US. The only way a company can have an unpaid intern in the US is if that intern does no productive work for the company - that is, they don't profit from the intern's labor. My understanding is that it's actually rare for tech companies to violate this law. But I have heard that it is common in the publishing industry. See: http://news.ycombinator.com/item?id=2412255
That is an exception - US interns just can't be "productive". FTA: "50 percent of graduating students had held internships". Face it, most of them will be doing unpaid clerical work. It will be "educational", in that they will gain valuable office skills, but it won't really be legal.
My point was that doing what you described is illegal.