The Geneva Conventions apply to soldiers and civilians who behave in a certain prescribed way. If they fail to behave in that way then applying the Conventions is discretionary. For example, Al Qaeda does not represent a signatory of the Conventions nor does it abide by the conventions in treatment of prisoners, treatment of civilians, how and where in establishes military facilities and association with a government. Therefore, the Conventions do not apply since the Conventions are narrowly focused on LEGAL combatants and civilians. Since they do not fall within anybody's interpretation of the Conventions, it is entirely voluntary that we open GITMO to ICRC and others.

So then we look for some other "controlling legal authority", to borrow a useful phrase from a man who undoubtedly knows. There are a few treaties that the USA has signed concerning basic human rights. There is also a presumption in our government that some sort of fundamental human rights are a fundamental aspect of humanity. There are a few laws but not many. These treaties, assumptions, and laws are what guides our federal court's decisions concerning treatment.

Curiously, the present administration has not argued the precedences of either Lincoln or FDR in court, as far as I know. Both of whom were far more arbitrary than the present administration.