The chemical reaction that occurs during burning is based on the ratio of the mass of air to fuel.
The density is much, much less at altitude than at lower levels so the mass of O2 available for the given amount of fuel is different.
When a flame is 'blown out' it is extinguished because the mixture required to support combustion is leaned to the point that combustion is no longer possible.
(I wonder if there is also an element of moving the point of combustion away from the fuel source faster than the flame front can propagate?)
Reducing the available O2 has the reverse effect, making the mixture richer. This can reach a point where combustion can't occur. How many have experienced a rich cut in a piston a/c? Or seen the demo of dropping a lit match into an oil drum filled with petrol (I was happy to see the film of it and never felt the need to try it at home)?
I think the point about depressurising is a good one. Even if it doesn't completely extuingish the fire it will certainly reduce its intensity & rate of spread.
[This message has been edited by Tinstaafl (edited 28 April 2001).]