There have also been some arguments about whether "people" without any qualifier should refer

Yes, quite; there's room for reasonable disagreement about whether the first amendment protects the rights of assembly and petition only for citizens, for any subjects, or for anyone generally. But the protections for speech and the press (ie the ones actually relevant to Assange) have no such qualification. If they were prosecuting him for, say, standing in front of a government building yelling "Down with the NSA!", the fact that he's not a citizen would arguably be in any way relevant.