I have my doubts about compressed air feeding an external fire. It isn't going to create any kind of lasting overpressure, so it won't cause a significantly higher concentration of oxygen molecules as a general matter.
A jet of compressed air could certainly mix air into an oxygen-deprived area of hot gas and cause a flashover. But a jet of nitrogen would entrain air and cause general mixing, and might be almost as effective at causing flashover.
Compressed air could scatter burning fuel, especially if it's liquid. So could nitrogen.
I'm not sure about fire risk *inside* the tire. Compressed air isn't anywhere near the combustion threat of oxygen -- for example there's no strict prohibition on using oil on compressed air equipment there way there is with oxygen. I think that's because there are more oxygen molecules than with air at atmospheric pressure, but also a correspondingly higher number of nitrogen molecules to absorb heat and generally get in the way. On the other hand, if there's any internal fire risk at all from compressed air, it's infinitely higher than that from nitrogen.