Earlier quoted context omitted.
(Tedious disclaimer: my opinion, not my employers. Not representing anybody else. I work at Google, not on chrome) Google does not "track the full browsing experience of chrome users". Please read the privacy policy which is very clear on this subject: https://www.google.com/chrome/browser/privacy/ I particularly draw your attention to this paragraph: "If you use Chrome to access other Google services, such as using…
Maybe i'm reading this wrong, but this sounds like Google gets your browsing history: "If you sign in to Chrome browser, Chrome OS or an Android device that includes Chrome as a preinstalled application with your Google Account, this will enable the synchronization feature. Google will store certain information, such as HISTORY, bookmarked URLs as well as an image and a sample of text from the bookmarked page, passwo…
The fact that Google synchronizes data between browsers does not necessarily mean their search application has access to it as a ranking signal.