Now the thing is, Luigi when informed that he was under some sort of "official investigation" and that Detwiler believed he used a fake name Luigi promptly and immediately gave his real name.
Luigi later explained that he was homeless and simply provided what ID he had, which was fake.
Why the interaction didn't end with Luigi simply being allowed to leave McD's (possibly minus a fake ID) legal experts aren't sure.
That is until we read about the Supreme Court case Detwiler lost...