I had always assumed that all of them shared the pseudonym of Satoshi, along with Nick Szabo.

Back wrote the white paper with input from Hal and Nick Szabo. Sassaman did the coding work on the client. Sassaman had the keys to the Satoshi wallet, hence it never moving since his passing.

Since Satoshi is a collective, it means that each of them individually can claim, without lying, that they're not Satoshi.

That's my uninformed guess.