The article is light on details, but based on the way they talked about it ("impossible to hack in principle") it's likely that they actually can _prove_ that it's more secure than a Linux distro dedicated to security insofar as they're able to prove anything at all. Since the Linux APIs are not formally specified, or verified, it's essentially impossible to _prove_ anything at all (again, in a formal sense). Formal verification can get esoteric quickly, but the state of the art is very impressive (see CompCert, seL4, Agda, Idris).

As someone who has been paying attention to this space for some time I welcome anything new that increases exposure. It's cool stuff, and it's probably the future. However, there's a long way to go. Security doesn't stop at the operating system. In fact, the vast majority of security breaches occur due to misconfiguration, bugs, or good old fashioned social engineering. To really build a system that's "secure in principle" you can't stop at the operating system: you need to build a toolchain that makes it easy to build user space applications that are also "secure in principal" and you need to work on the HCI so the security model makes sense / isn't defeated by users. That's going to be a lot of work!