Visa-free transit

I have a NZ passport. I have a flight from Spain to Shanghai, then a separate flight from Shanghai to Melbourne which leaves 56 hrs later. This flight to melbourne stops in Chengdu (Sichuan airlines) for <2hrs.
1. Is it OK to get a free transit even thought I have a short layover in Chengdu on the way out?
2. If not, if I buy a flight straight from Shanghai to Melbourne instead, is that OK?
3. The NZ Chinese embassy said 'Visa is required. You do not eligible for free transit through Shanghai.' (very short email reply). Why?
I'm very confused!