Well, duh-uuh. Not every country that begins (in English) with "S" does whatever terrorists want it to do. I saw the video of the fellow and it's just heart-wrenching, but responding to videos shot at gunpoint is no way to run a government.
How could they have done it differently? Easy - something like "South Korea reasserts troop commitment despite kidnapping". A stronger action verb, different phrasing. I suppose it depends on your point of view, though, doesn't it?