Xiaotung AirNZ ignores various elements of *A policy as it chooses. For example, the T&C of Airports requires that only one ff# can be entered into a booking.
So, as a TG*G member, wanting to accrue into Airpoints (no status then) meant that Lounge access was not allowed, I even tried waving my TG*G card politely in CHC but was firmly denied access until they had replaced my TG*G with my NZ ff#. They did allow this until around 2014-15, as the system has fields FQTV (for accrual) and FQTS (for status) and so two different ff#s can be entered.
I queried AirNZ by email on this, noting that *A policy stated that access to *A branded lounges only required me to present my *G. Further, other *A airlines had no issue accruing to one program whilst using the status of another - indeed that seemed to me to be the point of the Alliance. The response was that I either had my Airpoints ff# or another ff#, but if Airpoints ff# used then I couldn't access the benefits of the other program. I finally asked if I could enter my SQ ff# into an NZ booking, and present my TG*G card to access the lounge, and it was agreed that this could be allowed on the basis that Airpoints was not involved.