Quite right, the "big fans" only use the "cold" air in the reverse mode but the exhaust (at 600C) from the core is still coming out ther back!
My point is that it only takes one spark ( or contact with this core stream) to set the whole lot off. The effect of the reversers at slow speed is to pick up everything (including in this case whatever was around the leak area) and deflect it forwards.
If you look at the 777 fire at Denver (on the ground) it was not initially direct contact between the leaking fuel connection and the engine exhaust cone but fuel vapour which then spread to the leak.
Back to the topic, they did a good job, any comments should be directed to those involved some fifty odd sectors earlier.