Sorry but you're wrong too.
Supplemental oxygen has been shown to increase performance in well trained runners.
Why?
Because well trained runners typically have what's called exercise induced arterial hypoxemia. Essentially, because of their large cardiac outputs the bloods whizzing through that full diffusion can not occur.
That's why you see oxygen saturation levels drop. When given supplemental oxygen, it returns these saturation levels to normal and improves performance. Why? Because it creates a larger pressure differential between the outside air and that in the blood stream. The oxygen cascade is increased.
I'm not saying the tree theory is correct as it sounds crazy to me. I've never seen anything showing oxygen concentrations in forests.
But the idea that oxygen intake is not a factor in performance is not true.
With cyclists:
http://www.springerlink.com/content/063346762241032g/