It is true that most fires do take hold very quickly and on occasion the `local` fire appliance might be out of area. This scenario you mention would suggest that both of the Devonport appliances and the Takapuna appliance were unavailable. It would be unlikely that the Birkenhead appliance would have responded from their own station but more likely have been on a cover move to Takapuna. That is still a fair travel down to Devonport and would certainly have allowed ANY fire to increase in size.
Anthony