I mean yes, obviously if you are in possession of a private key then you have the ability to move and spend the relevant coins. But that does not make you the original owner of those coins nor does it change that what you are doing is theft.

I am reminded here of the conversations about known fraud CSW not signing a message from the genesis block coinbase address. Obviously he can't because he is not Satoshi, but even if he could, such a message would only prove ownership of that key and would not prove he was Satoshi. Such a signed message is a necessary minimum to even start the conversation, but it is not proof of identity on its own.

For the record, I am firmly against any KYC for addresses or other such nonsense to prove ownership as has been mentioned in this thread. OP owns the private key and so can now take the coins if he choose. There should be nothing at a technical level to stop that from happening, but I am still of the opinion that doing so is theft.