It is obvious that Google somehow uses data from Google analytics for ranking a site. Do you think if everybody switched to another stats counter Google's SERPs would change significantly?
I understand that google may use the data from analytics. But I don't believe they have high impact on the SERPs. There are stil high quality websites in the top of search results which don't use analytics. And google cannot expect that 100% websites will use their stats. So they must be able to rank the websites without there data.