The only circumstance where they might be likely to decline a wall insulation request would be something like brick veneer where the insulation would be likely to interfere with the drainage plain. In other cases, where you make an alteration you are generally required to bring the area up to current standards which might require adding building paper or other moisture barrier.
That had been my assumption before I was turned down. I wasn't expecting to have the application declined on a 1927 timber house, but it was.
From what I gather, mainly from the Dept of Building and Housing guidance Doc on the subject that you quoted from earlier , the local authorities have discretion over whether a building consent for retrofit wall insulation is required or not so it may come down to the local opinions on the issue and also the climate in that area.
From my experience weatherboards rot because of either bulk water infiltration or defects in the outer surface that absorb moisture and decay over time. Insulation is unlikely to exacerbate either of these scenarios.
In my area a consent wasn't required but I was doing the work from the outside ie removing weatherboards, adding ply and building paper and a rainscreen in some areas, then reinstating or replacing weatherboards as appropriate. They were more interested, consent wise, if the work was done from the inside which I presume was related to the need to add a moisture barrier.