The inspector can only offer his "opinion" on the day.
You are right to appeal it but it looks like a case of the NHBC siding with Linden Homes.
Regarding the crack, the inspector should not have been so dismissive. Cracks are not only caused by 'settlement', they are caused by movement, which can be differential or thermal as well as subsidence.
The crack has re appeared because a movement joint was not allowed for, or built correctly.
It could also be as a result of a lack of localised reinforcement in the render - both as per manufacturer's instructions yet not being adhered to.