I think the ring must have been his good luck charm or something, but in his heightened state of emotions I can see where this is possible. He is suffering from a lot of stress from the war and wanted to keep something in his life intact.
This is possible that due to the emotional stress of the situation a person may not think rationally but where the hell were the doctors brains at that amputated his finger? The ring can be replaced but the finger can't. Just too idiotic for my liking but again this is the same mentality that brought you the Jessica Lynch story.
Will