Yes, Ohakea is big enough for an A340, but it is also New Zealand's only fully operational air force base, and is available to commercial aircraft only in an emergency.
Not it is not available only in an emergency!
Ohakea has been used since 1995 by Air New Zealand as an alternate and later by other airlines too. It's the whole reason Ohakea got/maintains Part 139 certification. The RNZAF garners revenue from airlines (you have to pay to be able to nominate Ohakea plus a movement fee should you actually use it).
I don't know the details, but I suspect the forecast for this flight indicated reasonable conditions for the planned ETA. Consequently, Ohakea was planned as the alternate. The aircraft subsequently arrived at Auckland, was unable to land due to unforecast inclement conditions and then diverted to the planned alternate. Honestly, is that such a big deal??
I concur completely with your thinking.