It was much too long and complicated to give a full answer here, but I have responded as to the several reasons why this doesn't make sense:
http://www.dotcult.com/does-google-analytics-affect-seo
That's a pretty good article on your blog. I think that it's likely that google will use the data from analytics more than you suggest, but I agree with you that many people put way to much into the idea of a google conspiracy.
Many people have this feeling that anything Matt Cutts says must be a lie to mislead everyone. That's always seemed a pretty funny idea to me, blackhatters aren't the only ones that reading and viewing googles press releases. The statements Google makes are intended for the regular whitehat webmasters and seo people. It wouldn't be in googles best interest to give out false information in the way the conspiracy theorists would have us believe.
Google is in the information business, they want to provide the most relevant results to searchers. If they help webmasters to make it easier for them to sort through all the websites, it just makes their job easier. If they give outright lies then the very websites they do want to show as most relevant will be presenting the wrong information, and the blackhatters that ignore the information would be the ones getting the best position. So outright lies would have the opposite effect of that which would be in googles best interest.
It's much more likely that the information that google releases is accurate, but probably in most cases not the complete story. I think they give out enough information to help people make the types of websites and do the types of seo they're looking for, but at the same time hold back enough information to prevent people from knowing too much about how to game the system. It's not so much a conspiracy, as just good business sense on their part.
Since the data in analytics is available to Google, I doubt that they would totally ignore it. I think if you have a whitehat site then GA is totally appropriate to use. I think it gives the webmaster some good information in a fairly simple layout, and any information that google might use themselves is more likely to be beneficial to your site. If you have a real spammy type site, or are running blackhat campaigns using your site, or doing a lot of blackhat seo then it just makes sense not to use analytics. As MisterGemini said, there are a lot of alternatives to GA that in many cases are superior to it. If you have anything you don't want to draw Googles attention to then it makes sense not to use their tools.
edit-
a few people pointed me to TheHockeyGod's reply so I feel I should make a note here. I believe TheHockeyGod is refering to someone else when he mentioned GrayWolf in his article. I imagine he was refering to Michael Gray's blog, if not then he meant someone else altogether. Anyone that has read many of my posts on bhw know that none of my replies ever really side one way or the other in regards to the google conspiracy theories.
The name I use here is GreyWolf, which is of course completely different than GrayWolf. LOL