I think it’s “provably secure” in the same sense that end to end chat apps can be provably secure. You can compare codes in the apps to prove that your conversation are noting man-in-the-middles. You still have to trust the software running on both ends to be doing the right thing.

Apple goes further than standard end-to-end encryption messaging by adding a software attestation component to the hand shake. And they say they will publish the server side software for researchers to poke at. And there is a certificate security style log so you can be sure that the server side software is published.

I’m not saying the system is good or works, I’m just saying don’t totally discount the idea of designing a system that has provable security properties.