Whether or not they are signatories is not germain to the argument - the US is a signatory.
Your legal system, including all of your rules of evidence, "rights", etc., is for whomever your government agrees to cover which may, or may not, include your citizens and those of other nations. Rule of law has nothing whatsoever to do with whether or not the people who are detained have ever signed a convention (individuals don't) or are citizens with rights (as opposed to either citizens without rights or non-citizens), but it has everything to do with the US government keeping its pledged word to the international community.
Bookmarks