Quite recently, we have had two Presidents claim that non-citizens had no right to challenge their imprisonment by the United States
No, the argument was that foreign terrorists and other non-state enemy combatants were not "subject to the jurisdiction" of the US legal system (because they weren't on US soil when captured, and as non-state combatants that weren't covered by any treaties to which the US was a party) and thus also not afforded its protections.
However, as a matter of international law, a country generally has legal jurisdiction over any person physically present in the country, whether present legally or otherwise, excepting specific diplomatic personnel (as defined by local law or treaty).
This was the reason for holding them indefinitely in an military facility located in another country. However, under US law, military facilities are considered US soil, and so persons being held in US military facilities are subject to the jurisdiction (and protection) of the US legal system.
No, the argument was that foreign terrorists and other non-state enemy combatants were not "subject to the jurisdiction" of the US legal system (because they weren't on US soil when captured, and as non-state combatants that weren't covered by any treaties to which the US was a party) and thus also not afforded its protections. However, as a matter of international law, a country generally has legal jurisdiction over any person physically present in the country, whether present legally or otherwise, excepting specific diplomatic personnel (as defined by local law or treaty).
This was the reason for holding them indefinitely in an military facility located in another country. However, under US law, military facilities are considered US soil, and so persons being held in US military facilities are subject to the jurisdiction (and protection) of the US legal system.