Boats if what you relayed is correct, it sounds like the Kims were poorly informed about what to expect in the wild. Following the river to civilization might make sense when you don't have a road; but in a mountainous area like that, in that weather, leaving the road was sheer madness.
While water will ultimately guide you to civilization, roads will usually do it faster. Roads also have the advantage of having travellers on them who can help you and better terrain for making good time. In a situation like this one where exposure is a very serious concern, I simply can't imagine leaving a road and crawling down a steep gully to walk along a streambed that obviously wasn't suited for walking.
The reports mentioned that SAR teams tracking Kim kept having to be pulled off the trail due to hypothermia from repeatedly falling into the river themselves. I can only imagine what it would be like in nylon pants, jeans and tennis shoes.
All of that makes me think hypothermia as I just can't imagine the desperation you would have to feel to make the decision that this course of action represented the best chance for your family, even if you didn't have much wilderness knowledge. Then again, it may be one of those decisions where it didn't look so tough at first and by the time Kim realized what he was into, it was too late to turn back.