Not a chemical reaction, and not a self-oxidizing fire. Further, one may not see flame, but one can still have combustion as a chemical process, producing heat, adequate to do substantial damage.
Ever seen a thermal runaway on a nicad battery?
The "fire triangle" was amended many years ago to become the fire tetrahedron, to include chemical interaction. Starving a fire of oxygen does not necessarily extinguish it right away, or at all, and may do little to stop the damage being done by the fire. Furthermore, a fire which is starved of oxygen still has heat, still has chemical interaction, and so long as fuel remains may progress in several ways.
Let's not let the perfect be the enemy of the good. If starving of oxygen kills 70-90% of cargo fires, it's better than what we have now. Chemical reactions are nasty, but they won't spread if the flammables nearby have no O2.
Beyond thermal runaway, I've seen a plane where the main NiCd battery exploded. Fortunately, it was while the MD-80 was being towed empty. That's one reason there are temperature sensors on NiCd batteries. Lead-acid batteries explode, too.
GB