There's nothing to claim, Satoshi can prove by signing a message, or moving his coins.
And that's what those claimers can't do.
A simple way to prove that they're satoshi.
But, they can't provide any signed message to prove that they're the owner of those bitcoins that satoshi has left, the real satoshi.
To be honest, I do not see the point of those people who claim that they are "satoshi" or anyone whatsoever. Aren't they just endangering and compromising their safety with such declaration? Are they just purely doing this for pride and for recognition around the world without even thinking the possible outcomes in the event that people do believe that you are satoshi?
Anyway, what you guys mentioned is the most easiest way of proving that you are indeed satoshi. If you can move the BTCs stored in his wallet address and personally sign a message, then you would be able to prove that you are indeed the almighty satoshi!