Just an idea. If Craig Wright is NOT Satoshi Nakamoto, he would definitely risk the real Satoshi come up with a proof, that Craig is not SN. Is it possible, that CW explicitly knows about the death of the person behind SN, so he can make his claims without backing them up with a proof?

you have a good point here because the way he claims the Name he is so sure about nothing will run unto Him,and also he is so confident about the claims.
but the Only Problem is he has no complete proof of being Satoshi so it means Him being Faketoshi.
the only way needs is the Address and also the Bitcointalk account that will Give him a chance to prove His claims.