If your contractor is thrown by a bit of close boarding I would reconsider letting them do anything to the top end of your house... not the most common roofing method but in no way unusual. Clay tiles presumably?
Concrete, done a few years ago, but I guess they left the sub-structure in place. That was my thoughts, so gone with another outfit who seem to know their onions.
Is this standard construction? The interior 'cladding'(?) seems to be throwing one of the contractors I spoke to.