A record of the cars history, ie liniage, is important when the owners are going through this process. History and proof with documentation of that history is only one of necessities in proving the cars authenticness. Existing parts are not the only critera. Cars like this along with those cars with alloy tubs have most likely had them replaced due to corrosion and damage. This is all documented in a restoration of a car of this significance.
There are many old race cars that go thru this process, ask John McKechnie and Bruce302 what the have been through and are going through with the proof they must submit. Parts are not the only critrea, after all how many race cars have their original engines.
I have not viewed C2 and to be truthfull I cannot comment on it.