The only scenario wherein Craig Wright could actually be Satoshi is if Satoshi had burned his bridges -- in the process of abandoning the Satoshi identity, he had deleted all cryptographic evidence of the identity; all private keys and credentials for online accounts.
In that case, if he later (now) decided to assert the identity, then he might be tempted to cobble together fake proof to get his foot in the door far enough that he could begin to assert various forms of social proof with people that he had interacted with while using the Satoshi identity.
It's worth noting that the "scorched earth" elimination of the Satoshi identity is another possible theory as to why nobody has credibly claimed the identity -- because even the individual (or group) that assumed the identity no longer has the ability to cryptographically assert that identity.