Gonz has hit on the real rationale: dry nitrogen is used to keep water
out of tires. Any one with experience with air compressors is aware
they do a good job of concentrating the residual humidity in the air
and it ends up condensed inside the storage tank and sometimes,
depending on how the system is plumbed in the air lines resulting in
some water inside the tire. Modern car tires have such low permeability
that this is an extremely minor concern, hence the opinions expressed
that the use of nitrogen is a scam. As others have pointed out if O2
preferentially leaks out then the content of the tire would drift in the
direction of higher and higher N2.