Maybe we should ask a vietnam vet if he feels less stress in nature than inside a building.
I think the reason we feel tense inside is because we've been conditioned to expect stressful situations to happen while inside, so we're on guard for it (ie tense). Nothing bad has ever happened to us while sitting on a park bench listening to the birds chirp. Now, if tigers start leaping out at us on a consistent basis while at the park, this feeling may change. We might decide the sounds of clicking keyboards and tapping shoes to be more relaxing.
Another point to consider is that the sounds of birds chirping means "things are ok". Bird have a high viewpoint compared to terrestrial animals and when birds are singing, there probably isn't a tiger stalking us. Also, if you notice, birds sing after storms pass. I know when I hear the birds singing, I can go back outside and get back to work... the storm is over. Its possible this knowledge is instinctual.
The same could be said of crickets and frogs. When you hear crickets and frogs, things are ok. When the crickets and frogs suddenly stop, that when you grab the flashlight and see what's lurking in the woods.
An odd one is the sound of water. If you're a prey animal, which humans would be in the wild, you'd have a large chance of being ambushed while getting a drink. All predators gather around the watering hole and stalk victims. So this raises the question... why are water sounds relaxing? This is evidence against instinct. Water sounds would be relaxing as a result of association rather than instinct. When I take a drink of water, I feel better. When I go fishing, I don't have to worry about anything but fishing. Water has always been good to me, so when I hear it, I feel better. Also, the sounds of water tends to drown-out other sounds. That's why spies on tv tend to have their conversations near moving water. There is something about the randomness of water sounds that won't allow pattern recognition in other sounds. When we hear water, its hard to be disturbed by other sounds, therefore, easier to be at peace.