I have never heard of the less oxygen claim. I have trouble believing that, even if there is less oxygen inside, it is enough to make a difference. As was already mentioned, how well the treadmill is calibrated can also make a big difference.
While I have always believed that running on a treadmill should be mechanically the same as running on the ground because you are moving relative to the surface in the same way, I recently came across this article that states differently. Interesting to consider.