I think Wolfram's claims are even more egregious than that.

His model is inherently computational. It would be like saying "here's a computer that can execute things" and then proving that you'd created the Linux kernel or something.

It's not a very surprising claim to say that a particular fact can be represented in a system which can represent anything. Mathematicians (well, most anyways) don't go around claiming they've discovered the secrets of the universe because math _could_ describe it in principle.