It doesn't explicitly forbid this, which is where the grey area tends to come into place. The official policy is to consider:
> The extent to which the intern’s work complements, rather than displaces, the work of paid employees while providing significant educational benefits to the intern.
The argument would be made that since the company is charging for work from unpaid interns to be fulfilled only by unpaid interns, it would be displacing the work of paid employees as opposed to complementing them. Of course, there's a lot more to it than just that going into the litmus test.