In this case, no one decided that. It's a habeas case.
Could you add some detail to what you said...clearly I am not up to speed.
Also the case law severely restricts what any president can do.
The German saboteurs who were executed during WWII were found to have been lawful detained under UCMJ, executive order, and Articles of War in ex parte Quirin(1942). Since then the US has ratified the 1949 Geneva Conventions which was held to apply to WOT detainees under Hamdan v. Runsfeld.