As far as I can see, Google provided a search-result, which eventually (after Google's batted it around internally a few times) turns into an HTTP request to the CBS website, which resulted in password-free access to a public document.

So that will show up in the CBS webserver's access log; that's how they got the IP address. Nothing to do with Google.

Getting from the IP address to the person is messier; websearches, requests to ISPs, and presumably searches of activist databases the cops no doubt maintain might all have played a part.

My guess is the cops knew there was no case against him, because they tried the URL, and saw that there was no password challenge; but charged him anyway, because he was an activist, and they wanted to intimidate him.