The Third Common Article of the Geneva Conventions reads (emphasis mine):
This is completely independent from the definition of Prisoners of War, which are defined under Article 4. This reads:
In the case of armed conflict not of an international character occurring in the territory of one of the High Contracting Parties, each Party to the conflict shall be bound to apply, as a minimum, the following provisions:
- Persons taking no active part in the hostilities, including members of armed forces who have laid down their arms and those placed hors de combat by sickness, wounds, detention, or any other cause, shall in all circumstances be treated humanely, without any adverse distinction founded on race, colour, religion or faith, sex, birth or wealth, or any other similar criteria. To this end the following acts are and shall remain prohibited at any time and in any place whatsoever with respect to the above-mentioned persons:
- violence to life and person, in particular murder of all kinds, mutilation, cruel treatment and torture;
- taking of hostages;
- outrages upon personal dignity, in particular, humiliating and degrading treatment;
- the passing of sentences and the carrying out of executions without previous judgment pronounced by a regularly constituted court affording all the judicial guarantees which are recognized as indispensable by civilized peoples.
- The wounded and sick shall be collected and cared for.
An impartial humanitarian body, such as the International Committee of the Red Cross, may offer its services to the Parties to the conflict.
The Parties to the conflict should further endeavour to bring into force, by means of special agreements, all or part of the other provisions of the present Convention.
The application of the preceding provisions shall not affect the legal status of the Parties to the conflict.
- Prisoners of war, in the sense of the present Convention, are persons belonging to one of the following categories, who have fallen into the power of the enemy:
- Members of the armed forces of a Party to the conflict, as well as members of militias or volunteer corps forming part of such armed forces.
- Members of other militias and members of other volunteer corps, including those of organized resistance movements, belonging to a Party to the conflict and operating in or outside their own territory, even if this territory is occupied, provided that such militias or volunteer corps, including such organized resistance movements, fulfil the following conditions:[
- that of being commanded by a person responsible for his subordinates;
- that of having a fixed distinctive sign recognizable at a distance;
- that of carrying arms openly;
- that of conducting their operations in accordance with the laws and customs of war.
- Members of regular armed forces who profess allegiance to a government or an authority not recognized by the Detaining Power.
- Persons who accompany the armed forces without actually being members thereof, such as civilian members of military aircraft crews, war correspondents, supply contractors, members of labour units or of services responsible for the welfare of the armed forces, provided that they have received authorization, from the armed forces which they accompany, who shall provide them for that purpose with an identity card similar to the annexed model.
- Members of crews, including masters, pilots and apprentices, of the merchant marine and the crews of civil aircraft of the Parties to the conflict, who do not benefit by more favourable treatment under any other provisions of international law.
- Inhabitants of a non-occupied territory, who on the approach of the enemy spontaneously take up arms to resist the invading forces, without having had time to form themselves into regular armed units, provided they carry arms openly and respect the laws and customs of war.
- The following shall likewise be treated as prisoners of war under the present Convention:
- Persons belonging, or having belonged, to the armed forces of the occupied country, if the occupying Power considers it necessary by reason of such allegiance to intern them, even though it has originally liberated them while hostilities were going on outside the territory it occupies, in particular where such persons have made an unsuccessful attempt to rejoin the armed forces to which they belong and which are engaged in combat, or where they fail to comply with a summons made to them with a view to internment.
- The persons belonging to one of the categories enumerated in the present Article, who have been received by neutral or non-belligerent Powers on their territory and whom these Powers are required to intern under international law, without prejudice to any more favourable treatment which these Powers may choose to give and with the exception of Articles 8, 10, 15, 30, fifth paragraph, 58-67, 92, 126 and, where diplomatic relations exist between the Parties to the conflict and the neutral or non-belligerent Power concerned, those Articles concerning the Protecting Power. Where such diplomatic relations exist, the Parties to a conflict on whom these persons depend shall be allowed to perform towards them the functions of a Protecting Power as provided in the present Convention, without prejudice to the functions which these Parties normally exercise in conformity with diplomatic and consular usage and treaties.
- This Article shall in no way affect the status of medical personnel and chaplains as provided for in Article 33 of the present Convention.
David is correct that the "insurgents" do not appear to fulfill the requirements to be considered prisoners of war. He is incorrect in asserting that the terms of Article 3 only apply to prisoners of war. The recent Supreme Court decision does not convey to the prisoners in Guantanamo Bay the priviledges of prisoners of war, but just the priviledges required by the Conventions for anyone no longer taking part in active hostilities.
The full text of the Third Geneva Conventions can be found on Wikisource.