Apologies I read the immediate heading under checked in baggage referring to fares, connecting flights etc and found the excerpt under number of bags.

Are you interpreting the part where it says where the ticketed itinerary has two or more Star Alliance airlines,..... as excluding single airline tickets??

Because I read "where" as being IF your ticket includes two or more carriers rather than ONLY IF you have 2 or more carriers.

There must be someone with *G (non NZ) that's flown even TT or Pacific Islands with NZ on a seat + bag or more fare and been allowed to take an extra bag. I'd think we would have had many complaints on this forum if that were the case. I mainly recall enquiries around the free bag with regards to the seat only fare.