Google is sure to use at least some part of the information it collects using Google Analytics for improving search engine results. They actually discover a lot about a site by providing this service.
This is complete paranoid bollocks. Data from GA plays no part in the serp s algorithm - how could when not all sites use it? Most significant major commercial sites use a paid service like Omniture or Webtrends, or their own proprietary tracking programme. You cannot use factors in a serps algorithm that you can't apply to all sites.
I like the numbers showed on Awstats, but I read Google analytics everyday. Awstats and GA need 24 hours to update , I am thinking to use the service as getclicky to get real time stats. Real time stats might be interesting.