Uh yeah. I'm assuming you know how HTTP works, but if not, _basically_ you send a request to GET content, and the server makes a decision on what/whether or not to return. If that user shouldn't be able to see the content because they haven't logged in then its up to the server to decide.
It's crazy to send them the content but tell them not to read it... back to your example would you expect your bank to do that? Here's all the account details and transactions but oops thats not your account. I'm guessing no, you'd hold your bank to a high technical standard.
To be clear, if newspapers/journalists want to work out some special agreement with google (or partner/agreed upon indexers) so their requests are authenticated so that only they have access to the content - i think that is a better solution then pay walls and sending the article and saying "don't read this please"