That's not part of this spec, all it says is that the attester produces a cryptographic proof. What it checks and what that proof means is for the attester to decide.

Google and Apple say they would "just" check if the user is logged into their Google/Apple account, as a way to proof that they are human and not a bot. That would be bad enough, because you should not have to have an account with these companies to browse the web. But they could easily make it even worse, by requiring you to install a kind of anti-cheat software that scans your device, and only provide the proof if they like the results. Heck they could just exclude everyone who visited a certain website in the past or who's name starts with an F if they wanted to, because that's how broad and dangerous this proposal is!

Big companies should not be able to decide if people are allowed to visit certain websites or not, even if they say they have the best intentions.