I wouldn't be too sure on the "negative on assistance" bit.
That comes from an ATC recording soon after the turn-around (not sure exactly when) when they are still something like 200nm from SIN still at FL170, i.e. before any descent into SIN. The crew wouldn't be thinking about ARFF equipment at that point. They might have interpreted the question as ATC asking if there is anything else they need right at the time.
They might well have asked for equipment closer in. We just don't know.