Google cannot be responsible for what it indexes.
They take it upon themselves anyway.
"Google regularly receives requests from copyright holders..."
[h=2]How many of these requests did you comply with?[/h] We removed 97% of search results specified in requests that we received between July and December 2011.
[h=2]How quickly do you remove search results after a request is made?[/h] We remove search results that link to infringing content in Search when it is brought to our attention, and we do it quickly. As of December 2012, our average processing time across all removal requests submitted via our web form for Search is approximately 6 hours. However, many different factors can influence the processing time for a particular removal request, including the method of delivery, language, and completeness of the information submitted.
[h=2]What is the DMCA?[/h] The DMCA or Digital Millennium Copyright Act is a U.S. law that provides qualifying online service providers like Google with a safe harbor from monetary liability for copyright infringement claims. One of the requirements of these safe harbor provisions is that the service provider remove or disable access to allegedly infringing material upon receiving a request that meets certain requirements. In responding to copyright removal requests, Google complies with the requirements of the DMCA.
[h=2]Do you only comply with the DMCA? What about other copyright laws?[/h] It is our policy to respond to clear and specific notices of alleged copyright infringement. The form of notice we specify in our web form is consistent with the DMCA and provides a simple and efficient mechanism for copyright owners from countries around the world.
[h=2]What is Chilling Effects?[/h] Chilling Effects is a joint project of several law school clinics, including at Harvard, Stanford, Berkeley, and the George Washington School of Law, and the Electronic Frontier Foundation. Chilling Effects posts and analyses copyright removal requests (among other types of content removal requests) from a number of participating companies on its website. We link in our search results to the requests published by Chilling Effects in place of removed content when we are able to do so legally.
...
Or you could just look around BHW and find threads starting with "So I just got a "Notice of DMCA removal from Google Search" because apparently my website was guilty of copyright infringement"
Obviously a copyright holder can pursue every avenue they wish: the hosting provider, the search engines, even the domain name (with federal help) and the court system in some cases.