Tourist, to pick nits, the heat exchanger that was blocked with ice is considered to be part of the engine (i.e. a fuel/engine oil heat exchanger). So yes, it can certainly be considered an "engine problem".
I'll be curious to hear if the wing fuel tank was penetrated, or if the fire was fed purely with "engine fuel". On a 777, shutting down the engine (either with the fuel switch or the fire handle) will close the spar valve. However, the spar valve takes a few seconds to close so if the fuel line is compromised the boost pumps can push a lot of fuel out in those few seconds (plus whatever crew reaction time there was).
In response to a previous post regarding containing disc failures - it simply isn't practical. There is way too much energy involved - even armor plate would be easily penetrated (while doing a rotor burst analysis on the 777, someone asked the question of "where would a 1/3 fan disc go" - the answer was "wherever it wants to"
).