In terms of privacy, Microsoft have far more invasive software within their operating systems last I checked. Basically they have the capability to report back the entire contents of your machine to their central server. If Apple couldn't do the same I would be surprised. Then there is all of the spyware which can easily creep onto your PC. Then there is the web and the numerous ways a machine can be compromised.
So compared to those privacy concerns, Amazon having the ability to look into my Kindle isn't a huge deal just yet. Theoretically they could do it, but at this stage they aren't using it to chase people over DRM issues, so it's not a big concern to me. If you have documents with valuable personal data I wouldn't keep them on the Kindle just in case*.
I think the other responses have answered the question pretty well!