I read it differently. All the combined brains of the technical department failed to spot symptoms of a problem that had been known about for a couple of years. So, if they didn't spot it, what chance did the pilot have with his limited resources (while managing an ailing aircraft at the same time)?
The bloke in charge of the fire service was accurate and up to date with his updates and was obviously very sensitive to the possibility that an evacuation via slides may not have been the safest option for the passengers. Presumably, he was aware of the potential danger of pooled, unburned fuel on the ground below the aircraft.
At no stage were the cabin crew calling like mad, telling the pilot there was heat. The pilot was busy attending to all the other things going on so the CC told their boss who told the IFS who can't remember if he passed that on to the flight deck. I would take that to mean "No, I didn't pass it on".
As for "shutting down an unhealthy engine"; that is discussed in the report and the answer seems to be that there was only 1 indication that was anything wrong, a low oil quantity alert. Other indicators showed it may be a defective indication as temperatures and oil pressures were OK.
The bottom line is not some sort of failure on the part of either the crew, the fire service or anyone else. The real culprit is the engine manufacturer who continued using the same fuel cooling system that had been shown to have failed more than once in the past. They had acknowledged this and issued a bulletin saying it should be checked the next time the engine is for maintenance and this was issued after the engine's last maintenance was done..