The moisture is bad for tires, not the 21% oxygen and a few trace gasses.
Compressed air from an air compressor contains moisture. A good shop air supply system will utilized an effective condensing system to remove most of it. A poor shop air supply system will have excessive moisture in the air supply which is damaging to air tools. I have seen moisture spray out of a air hose due to a poorly designed, neglected air supply system.
When the Nitrogen is introduced into the system, the moisture easily finds spaces to take up, seeking osmotic equilibrium until the moisture is equally distributed throughout the gas.
Using a vacuum pump to vaporize the moisture that is present in a empty car tire may damage the tire and is impractical. Remember that the soap and water solution that tire shops use to mount the tire does introduce moisture into the tire. An approved rubber lubricant containing no water should be used.
To do a good job of removing the moisture the tire is inflated with nitrogen then depressurized, the moisture is carried out with the departing Nitrogen. Then refill the tire.