Neither from them claims to be in possession of any digital proof, which would be a trivial and the only reasonable way to show that somebody actually has an access to any of Satoshi's keys.

And we, the general public, even have an access to two examples of something that was supposed to be a digital proof but it surely isn't, and that something was presented in a way to make the chance for verification as small (or the process slow) as possible (first example: the fake "Satoshi" PGP message, second case: the Sartre blog post). We see that the author is quite capable of presenting something as something that it isn't.