But how do they bypass the paywall? They can't just pretend to be Google by changing the user-agent, this wouldn't work all the time, as some websites also check IPs, and others don't even show the full content to Google.
They also cannot hijack data with a residential botnet or buy subscriptions themselves. Otherwise, the saved page would contain information about the logged-in user. It would be hard to remove this information, as the code changes all the time, and it would be easy for the website owner to add an invisible element that identifies the user. I suppose they could have different subscriptions and remove everything that isn't identical between the two, but that wouldn't be foolproof.