I gave a call to SK and they confirmed that there is no interline agreement with NZ,
Strange, that two Star Alliance longhaul carriers have no agreement on interlining baggage. It's baffling, because you can book CPH-PVG-AKL on the flysas.com website (SK to NZ connection)
I would assume the agent told you the wrong thing or didn't have a clue.
There might be an airport specific issue at PVG that prevents checking through baggage.