Remember also that the Air NZ group is the only airline in NZ with extensive experience operating around volcanic ash clouds in NZ airspace....although this is admittedly a different case, with a different type of cloud, there were several large eruptions of Mt Ruapehu in the central North Island during the late 90s. From memory, very few flights were cancelled.
Whatever the airline, I'm sure the PiC retains the final call...afterall, the pilots don't want to risk their lives either!