Checking the hash isn't relevant here. The content is served via HTTPS, you either trust the host or you don't. A host can easily serve you a malicious binary, as well as the valid hash of that malicious binary.
Most likely they get the precompiled rustc binary just like rustup, and LGTM-YOLO the package. If they try to be diligent, they maybe take extra 150K lines of mrustc code they can't reasonably carefully review for backdoors either, and then use it to bootstrap the several sets of 15M lines of code they won't look at.