The Law as it reads -

No matter how you cut the doctrinal legal sausage, captured means detain under humane conditions for the duration of hostilities - subject to concurrent trial before a competent tribunal for crimes under domestic and/or international law. Since just before WWI, US military law has prohibited summary executions. Before that, some US authority existed for summary executions if ordered by a field grade officer (e.g., Tony Waller was found not guilty for Samar; at about the same time, Breaker Morant was shot in South Africa for the same thing).

The Law as it (sometimes) is applied -

You all recall the Astan PMC (Don Ayala), bodyguard for Paula Loyd who was burned to death by a Astan villager. After the villager was handcuffed, Ayala executed him. The charge ended up being manslaughter, to which Ayala pled and was sentenced to probation by the Federal judge (post, And he got it ... ; and also, this prior post, Yup,).

The law on the books (doctrinal) is subject to the "law" in the decision-maker's noggin - the "quality of mercy, etc.".

Regards

Mike