Adam,
Now that I've had time to sit down and read over the past few days' discussion I'll respond:
I think describing any golf couse as "natural" is a bit counterintuitive. First off, golf courses notoriously promote growth of only a few species of plants (read: grass), which for most areas of the US is not natural.
Secondly, how many of the golden age golf courses in existance today still capture the true essence of what they were 80 years ago? Years of renovation, improvement, simplification and just growth have rendered most courses from that era to be the result of man's communion with nature and not nature itself.
Thirdly, pictures from that era can be misleading. They give no sense of depth or perspective really. In the images I've seen of Pine Valley, it would appear that the corridors used for golf were as natural as could possibly given the use for golf. I think the better question would be: If golf grass was natural here, what would this look like?
I do, however, agree that many modern architects get unfairly or blindly criticized for making things look too "man-made." This is golf, an invention of man: anything type of change to the ground for the purpose of playing the game will look man-made, because... it is.