Why could that be?
The gas inside a tyre is only there for one purpose - namely to keep the tyre from going flat (and specifically flat at the bottom as it is rare for a tyre to go flat at the top). The right pressure ensures that the correct area of rubber is in contact with the road and takes up some of the vibration from the uneven surface.
Air is 78% nitrogen already, and all but 1% of the remainder is oxygen, so what might be the advantage of going for a gas that you have to pay for instead of free air?
Nitrogen is very slightly lighter than air, so the 'moment of inertia' of the whole wheel might be reduced, but only by an unnoticeable amount. Nitrogen is dry whereas air contains a little moisture which might condense into a tiny droplet or two of water. So what? Certainly corrosion of wheels isn't such a massive problem. When did you last see a wheel rusted away from the inside. Why could that possibly be worse than the constant attack of the atmosphere on the outside of the wheel?
Some claim that oxygen molecules are smaller than nitrogen so it diffuses more easily through the rubber allowing the pressure of the tyre to vary from optimal more quickly. This is plain wrong. Oxygen is bigger and will diffuse more slowly (albeit not much bigger and not much more slowly).
It is also plain wrong to claim that oxygen expands and contracts more if the tyre temperature changes. Anyone claiming that is unaware of the 'gas laws' - basic physics taught to 15 year-olds.
There must be only one explanation for the recommendation to use nitrogen in tyres.
Surely it just another way to extract money from the gullible.
Small note: Or have I missed something else?
And yes - we really do spell the word tyre with a y in UK English.