Just because you can't see flames doesn't mean there aren't any.
If you can't see flames but only limited amount of smoke (hence not so dense you can't see through it), then it's hardly clearly catastrophic and there is time to think. - You don't come across as a pilot, but i can inform you that the pilots won't use half hours assessing a situation with smoke, just seconds. But thats also enough to - as in this case - establish if it is something that is under control and well known or something more serious and then take the appropiate actions.
THAT is the reason the Captain should have been informed, and passenger injuries would most likely have been non-existent.
In reality i don't think it is the CC that fails here, but the company for not training them well enough to do the job they do.
IMHO as humble SLF, the CC played it safe, which is the correct thing to do. I thought the whole ethos of flying was safety first, not protocol.
Talking in hindsight about any crew communication issues..... communication goes both ways... maybe the FD crew could have told the CC that the problem had been identified and was being resolved ?
It is not "playing it safe" when people get injured for no reason at all, and the protocol is there for exactly that reason: "Play it safe"
How could the FD communicate that the problem was under control when they were never involved in the process from the CC? we don't tell them about every little technical fault for a various of reasons, but they probably would have been told if they took the interphone and informed that "we have some smoke development in the rear", what do you want us to do? - and take it from there.