I doubt they own all of the links they use worldwide, but Google did go on a buying binge a few years ago, acquiring large amounts of "dark fiber". There's some discussion about that whole topic here:

http://www.howstuffworks.com/tech-myths/5-myths-about-google...

http://news.cnet.com/Google-wants-dark-fiber/2100-1034_3-553...

http://www.lightreading.com/document.asp?doc_id=633236