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I'm not too worried about it for a couple of reasons. First off, the Silk browser is only used on the Kindle Fire, and I see that as primarily a toy/entertainment tablet, so there isn't going to be a huge stream of confidential data going out from it. I also looked at the response from Amazon to an inquiry from a congressman about whether the Silk Browser would violate user privacy. Amazon says that it will only aggregate browsing activity across all users and it would not link browser use to any individual Kindle Fire users. Web content is only cached if the site owner has enabled caching and only content that has been specifically IDed.
The upside to Amazon use of its cloud infrastructure is that it speeds up surfing by pre-fetching and pre-rendering content and website caching. One other thing that I didn't know until I read Amazon's response was that all traffic between Amazon Web Services and the fire is encrypted, which is actually a nice little security gain for the user. So while maybe I'm being too trusting or perhaps have just accepted that privacy as we used to know it is a thing of the past, and I'm not very concerned about this issue.